In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morre...In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morrey-Campanato spaces are obtained.展开更多
The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boun...The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.展开更多
In this paper,we consider the solutions of 2-D incompressible magnetohydrodynamic(MHD)equations with homogenous Dirichlet boundary condition for velocity and with nonhomogenous Dirichlet boundary condition for magneti...In this paper,we consider the solutions of 2-D incompressible magnetohydrodynamic(MHD)equations with homogenous Dirichlet boundary condition for velocity and with nonhomogenous Dirichlet boundary condition for magnetic field.We obtain a condition of boundary layer separation by Taylor expansion of functions in the MHD equations and by structural bifurcation theory for divergence free flows with Dirichlet boundary conditions.Furthermore,the condition,determined by external forces,initial values and the value of magnetic field on the boundary,can predict when and where boundary layer separation for the magnetic fluid will occur.展开更多
In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic （MHD） equations. Such solutions can be explicitly expr...In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic （MHD） equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations axe directly constructed.展开更多
In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval[O,T].Five sufficient couditions are gi...In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval[O,T].Five sufficient couditions are given.Our results are motivated by two main ideas:one is to control the accumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.展开更多
In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions t...In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.展开更多
The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighte...The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author＇s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ〉1.展开更多
This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature vari...This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.展开更多
In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations.We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform conver...In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations.We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic equations.It turns out to be robust for relatively large physical parameters.By extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.展开更多
In this paper, we are concerned with Cuuchy problem for the multi-dimensional （N 〉_ 3） non-isentropic full compressible magnetohydrodynamic equations. We prove the existence and unique- ness of a global strong solu...In this paper, we are concerned with Cuuchy problem for the multi-dimensional （N 〉_ 3） non-isentropic full compressible magnetohydrodynamic equations. We prove the existence and unique- ness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces. Our method is mainly based on the uniform estimates in Besov spaces for the proper linearized system with convective terms.展开更多
We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev...We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev inequalities of logarithmic type,we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded.Our result is the same as Ponce’s criterion for 3D incompressible Euler equations.In particular,it is independent of the magnetic field and temperature.Additionally,the initial vacuum states are allowed.展开更多
Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.
In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperat...In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.展开更多
We investigate the local existence of smooth solutions of a 3D ideal magneto-hydrodynamics （MHD） equations in a bounded domain and give a blow-up criteria to thisequations with respect to vorticists.
In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired ...In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.展开更多
In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, ...In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.展开更多
We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and il...We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t = 0. The strong convergence results only hold outside the initial layer.展开更多
The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least sq...The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of its solution are derived. Through this method, the combination among the mixed finite element spaces does not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.展开更多
A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.
The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we disc...The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we discretize in time using the linearly backward differentiation formula,and by employing both the discrete Gronwall lemma and the discrete uniform Gronwall lemma,we establish that each numerical scheme is uniformly bounded in the H^(1)-norm.展开更多
基金supported in part by the NNSF of China (11101144,11171377)Research Initiation Project for High-level Talents (201031) of North China University of Water Resources and Electric Power
文摘In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morrey-Campanato spaces are obtained.
基金supported by NSFC(11371042)China 973 program(2011 CB808002)+2 种基金BSFC(1132006)CIT&TCD(20130312)the fund of the Beijing Education Committee(KZ 201210005005)
文摘The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.
基金Supported by the National Natural Science Foundation of China(Grant No.12171343)the Scientific Research Fund of the Science and Technology Department of Sichuan Province(Grant No.22CXTD0029)。
文摘In this paper,we consider the solutions of 2-D incompressible magnetohydrodynamic(MHD)equations with homogenous Dirichlet boundary condition for velocity and with nonhomogenous Dirichlet boundary condition for magnetic field.We obtain a condition of boundary layer separation by Taylor expansion of functions in the MHD equations and by structural bifurcation theory for divergence free flows with Dirichlet boundary conditions.Furthermore,the condition,determined by external forces,initial values and the value of magnetic field on the boundary,can predict when and where boundary layer separation for the magnetic fluid will occur.
文摘In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic （MHD） equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations axe directly constructed.
基金The first author is partially Supported by Natural sciences Foundation of china(No.10101014)Beijing Education Committee Foundation and the Key Project of NSFB-FBECThe second author is partially supported by Natural Sciences Foundation of China
文摘In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval[O,T].Five sufficient couditions are given.Our results are motivated by two main ideas:one is to control the accumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.
基金supported by National Natural Science Foundation of China(Grant Nos.11971477,11761141008,11601128 and 11671319)the Fundamental Research Funds for the Central Universities+3 种基金the Research Funds of Renmin University of China(Grant No.18XNLG30)Beijing Natural Science Foundation(Grant No.1182007)Doctor Fund of Henan Polytechnic University(Grant No.B2016-57)completed when Yaobin Ou visited Brown University under the support of the China Scholarship Council(Grant No.201806365010)。
文摘In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.
基金Supported by National Natural Science Foundation of China (Grant No. 11101043)
文摘The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author＇s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ〉1.
基金supported by National Natural Science Foundation of China(Grant Nos.11971477,12131007 and 11761141008)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.18XNLG30)。
文摘This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.
基金supported in part by the National Science Fund for Dist inguished Young Scholars 11725106,China NSF grant 11831016.
文摘In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations.We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic equations.It turns out to be robust for relatively large physical parameters.By extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.
基金Supported by National Natural Science Foundations of China(Grant Nos.11501332,11171034 and 11371221)Natural Science Foundation of Shandong Province(Grant No.2015ZRB01718)+3 种基金China Postdoctoral Science Foundation funded project(Grant No.2014M561893)the Open Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin,China Institute of Water Resources and Hydropower Research Fund(Grant No.IWHR-SKL-201407)the Specialized Research Foundation for the Doctoral Program of Higher Education of China(Grant No.20123705110001)the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province
文摘In this paper, we are concerned with Cuuchy problem for the multi-dimensional （N 〉_ 3） non-isentropic full compressible magnetohydrodynamic equations. We prove the existence and unique- ness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces. Our method is mainly based on the uniform estimates in Besov spaces for the proper linearized system with convective terms.
基金partially supported by National Natural Science Foundation of China(Nos.11901474,12371227)。
文摘We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev inequalities of logarithmic type,we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded.Our result is the same as Ponce’s criterion for 3D incompressible Euler equations.In particular,it is independent of the magnetic field and temperature.Additionally,the initial vacuum states are allowed.
基金J.Fan is partially supported by NSFC(No.11171154)Ju is supported by NSFC(Grant Nos.12071044,12131007).
文摘Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.
基金supported by the National Natural Science Foundation of China(No.11931013)the Natural Science Foundation of Guangxi Province(No.2022GXNSFDA035078)the Foundamental Research Funds for the Central Universities,CHD(No.300102122115).
文摘In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.
基金supported by NRF-2015R1A5A1009350the National Research Foundation of Korea Grant funded by the Korean Government(NRF-2016R1D1A1B03930422)
文摘We investigate the local existence of smooth solutions of a 3D ideal magneto-hydrodynamics （MHD） equations in a bounded domain and give a blow-up criteria to thisequations with respect to vorticists.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Foundation(202203021211129)。
文摘In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.
基金Supported by the National Natural Science Foundation of China(11671134)
文摘In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.
基金supported by Postdoctoral Science Foundation of China through Grant 2017M610818
文摘We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t = 0. The strong convergence results only hold outside the initial layer.
基金Project supported by the National Natural Science Foundation of China (Nos.10471100 and 40437017)the Science and Technology Foundation of Beijing Jiaotong University
文摘The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of its solution are derived. Through this method, the combination among the mixed finite element spaces does not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.
基金Project supported by the National Natural Science Foundation of China (Nos.10471100 and 40437017)
文摘A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.
文摘The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we discretize in time using the linearly backward differentiation formula,and by employing both the discrete Gronwall lemma and the discrete uniform Gronwall lemma,we establish that each numerical scheme is uniformly bounded in the H^(1)-norm.
