This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of th...This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.展开更多
This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn i...This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.展开更多
For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are...For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H^3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H^3 and bounded in L6/5.展开更多
The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the follo...The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the following sense： we extend the class of pressure functions, that is, we consider lower exponent γ.展开更多
It is well known that the full compressible Navier-Stokes equations with viscosity and heat conductivity coefficients of order of the Knudsen number ò>0 can be deduced from the Boltzmann equation via the Chapm...It is well known that the full compressible Navier-Stokes equations with viscosity and heat conductivity coefficients of order of the Knudsen number ò>0 can be deduced from the Boltzmann equation via the Chapman-Enskog expansion. In this paper, we carry out the rigorous mathematical study of the compressible Navier-Stokes equation with the initial-boundary value problems. We construct the existence and most importantly obtain the higher regularities of the solutions of the full compressible Navier-Stokes system with weak viscosity and heat conductivity in a general bounded domain.展开更多
We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the c...We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results,the delicate global phase plane analysis,based on the qualitative theory of ODEs,is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic,transonic,and subsonic regions,respectively,which completely answers the existence/nonexistence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.展开更多
The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA00...The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA0012 airfoil is used to verify the efficiency of the proposed method. Two cases of the low Mach number flows around the multi-element airfoil and the circular cylinder are also used to test the proposed method. Numerical results show that the methods combined the preconditioning method and compressible Navier-Stokes equations are efficient to solve low Mach number flows.展开更多
This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational fo...This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.展开更多
In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in s...In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.展开更多
In this paper,we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity,analogous to the Beal-Kato-Majda criterion for the idea...In this paper,we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity,analogous to the Beal-Kato-Majda criterion for the ideal incompressible flow.In addition,the initial vacuum is allowed in our case.展开更多
A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is establishe...A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.展开更多
The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove...The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.展开更多
In this paper,we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-di...In this paper,we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum,across which the density changes discontinuosly.Smoothness of the solutions and the uniqueness of the weak solutions are also discussed.The present paper extends results in Luo-Xin-Yang[12] to the jump boundary conditions case.展开更多
We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-Ⅰ singularities of solutions with■ can never happen at time T for all adiabatic number γ 1. Here ...We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-Ⅰ singularities of solutions with■ can never happen at time T for all adiabatic number γ 1. Here κ > 0 does not depend on the initial data.This is achieved by proving the regularity of solutions under■ This new scaling invariance also motivates us to construct an explicit type-Ⅱ blowup solution for γ > 1.展开更多
The zero dissipation limit of the compressible heat-conducting Navier–Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coeffici...The zero dissipation limit of the compressible heat-conducting Navier–Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ = O（ε）, κ/ε≥ c 〉 0, as ε→ 0 （see （1.3））, if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier–Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].展开更多
In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity ...In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.展开更多
A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and...A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.展开更多
A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable...A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition. An error estimate is Obtained.展开更多
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate...We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.展开更多
基金supported by the Program for New Century Excellent Talents in University of the Ministry of Education(NCET-13-0804)NSFC(11471127)+3 种基金Guangdong Natural Science Funds for Distinguished Young Scholar(2015A030306029)The Excellent Young Teachers Program of Guangdong Province(HS2015007)Pearl River S&T Nova Program of Guangzhou(2013J2200064)supported by the General Research Fund of Hong Kong,City U 104511
文摘This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.
基金supported in part by the NSF of China (10571024,10871040)the grant of Prominent Youth of Henan Province of China (0412000100)
文摘This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.
基金Sponsored by National Natural Science Foundation of China (10431060, 10329101)
文摘For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H^3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H^3 and bounded in L6/5.
基金supported by National Natural Science Foundation of China-NSAF(11271305,11531010)the Fundamental Research Funds for Xiamen University(201412G004)supported by National Natural Science Foundation of ChinaNSAF(11271305,11531010)
文摘The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the following sense： we extend the class of pressure functions, that is, we consider lower exponent γ.
文摘It is well known that the full compressible Navier-Stokes equations with viscosity and heat conductivity coefficients of order of the Knudsen number ò>0 can be deduced from the Boltzmann equation via the Chapman-Enskog expansion. In this paper, we carry out the rigorous mathematical study of the compressible Navier-Stokes equation with the initial-boundary value problems. We construct the existence and most importantly obtain the higher regularities of the solutions of the full compressible Navier-Stokes system with weak viscosity and heat conductivity in a general bounded domain.
基金partially supported by the NSFC(12171459,12288201,12090014,12421001)CAS Project for Young Scientists in Basic Research(YSBR-031)。
文摘We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results,the delicate global phase plane analysis,based on the qualitative theory of ODEs,is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic,transonic,and subsonic regions,respectively,which completely answers the existence/nonexistence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.
文摘The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA0012 airfoil is used to verify the efficiency of the proposed method. Two cases of the low Mach number flows around the multi-element airfoil and the circular cylinder are also used to test the proposed method. Numerical results show that the methods combined the preconditioning method and compressible Navier-Stokes equations are efficient to solve low Mach number flows.
基金Program for New Century ExcellentTalents in University(NCET-04-0745)the Key Project of the National Natural Science Foundation of China(10431060)
文摘This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.
文摘In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.
基金supported in part by Zheng Ge Ru Foundation,Hong Kong RGC Earmarked Research Grants(Grant Nos.CUHK4028/04P,CUHK4040/06P,CUHK4042/08P)the RGC Central Allocation Grant(Grant No.CA05/06.SC01)
文摘In this paper,we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity,analogous to the Beal-Kato-Majda criterion for the ideal incompressible flow.In addition,the initial vacuum is allowed in our case.
基金partially supported by NSFC (10825102)for distinguished youth scholarsupported by the CAS-TWAS postdoctoral fellowships (FR number:3240223274)AMSS in Chinese Academy of Sciences
文摘A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.
文摘The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.
文摘In this paper,we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum,across which the density changes discontinuosly.Smoothness of the solutions and the uniqueness of the weak solutions are also discussed.The present paper extends results in Luo-Xin-Yang[12] to the jump boundary conditions case.
基金supported by National Natural Science Foundation of China (Grant No. 11725102)National Support Program for Young Top-Notch Talents+3 种基金SGST 09DZ2272900 from Shanghai Key Laboratory for Contemporary Applied Mathematicssupported by Zheng Ge Ru Foundation, Hong Kong RGC Earmarked Research Grants (Grant Nos. CUHK-14305315, CUHK-14300917 and CUHK-14302917)NSFC/RGC Joint Research Scheme Grant (Grant No. N-CUHK 443-14)a Focus Area Grant from the Chinese University of Hong Kong
文摘We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-Ⅰ singularities of solutions with■ can never happen at time T for all adiabatic number γ 1. Here κ > 0 does not depend on the initial data.This is achieved by proving the regularity of solutions under■ This new scaling invariance also motivates us to construct an explicit type-Ⅱ blowup solution for γ > 1.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘The zero dissipation limit of the compressible heat-conducting Navier–Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ = O（ε）, κ/ε≥ c 〉 0, as ε→ 0 （see （1.3））, if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier–Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].
基金supported by China Postdoctoral Science Foundation(2012M520205)supported by National Natural SciencesFoundation of China(11171229,11231006)Project of Beijing Chang Cheng Xue Zhe
文摘In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.
文摘A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.
基金Project supported by the Science and Technology Foundation of Sichuan Province (No.05GG006- 006-2)the Research Fund for the Introducing Intelligence of University of Electronic Science and Technology of China
文摘A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition. An error estimate is Obtained.
基金supported by National Natural Science Foundation of China (11001090)the Fundamental Research Funds for the Central Universities(11QZR16)
文摘We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.
