We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navi...We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navier-Stokes equations for(ρ,u)through a drag force term n(w−u).We prove the global existence of strong solutions to the coupled system when the initial data are small perturbations of the constant equilibrium state.However,due to the pressureless structure,one can only deal with the density n of the pressureless flow through the transport equation and it is crucial to obtain the exact time-decay rates for the corresponding velocity w of the pressureless flow.To this end,we make use of the spectral analysis,low-high frequency decomposition and time-weighted energy method to deduce the large time behavior of(w,ρ,u)and consequently establish the Lyapunov stability of the density n in Sobolev space.展开更多
In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a b...In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.展开更多
In this paper,we consider the Cauchy problem of the isentropic compressible Navier-Stokes equations with degenerate viscosity and vacuum inℝ,where the viscosity depends on the density in a super-linear power law(i.e.,...In this paper,we consider the Cauchy problem of the isentropic compressible Navier-Stokes equations with degenerate viscosity and vacuum inℝ,where the viscosity depends on the density in a super-linear power law(i.e.,μ(ρ)=ρ^(δ),δ>1).We first obtain the local existence of the regular solution,then show that the regular solution will blow up in finite time if initial data have an isolated mass group,no matter how small and smooth the initial data are.It is worth mentioning that based on the transport structure of some intrinsic variables,we obtain the L^(∞)bound of the density,which helps to remove the restrictionδ≤γin Li-Pan-Zhu[21]and Huang-Wang-Zhu[13].展开更多
本文证明带有临界型阻尼项的Navier-Stokes方程在Lei-Lin-Gevrey空间Xa,σ0(ℝ3)中存在唯一的局部解。文章利用不动点定理和热方程解的有关性质来证明这一主要结论。In this paper, it is proved that the Navier-Stokes equation with c...本文证明带有临界型阻尼项的Navier-Stokes方程在Lei-Lin-Gevrey空间Xa,σ0(ℝ3)中存在唯一的局部解。文章利用不动点定理和热方程解的有关性质来证明这一主要结论。In this paper, it is proved that the Navier-Stokes equation with critical damping terms has a unique local solution in the Lei-Lin-Gevrey space Xa,σ0(ℝ3). In this paper, the main conclusion is proved by using the fixed point theorem and the related properties of the solution of the heat equation.展开更多
The existence and uniqueness of stationary solutions to anisotropic Navier-Stokes equations is investigated by a Galerkin technique in this work.Based on this conclusion,we further explore the exponential stability of...The existence and uniqueness of stationary solutions to anisotropic Navier-Stokes equations is investigated by a Galerkin technique in this work.Based on this conclusion,we further explore the exponential stability of weak solutions to stochastic anisotropic NavierStokes equations.We present a relationship among different growth exponents,which is sufficient to guarantee the existence,uniqueness and exponential stability of stationary solutions.展开更多
We investigate a sufficient condition,in terms of the azimuthal componentω^(θ)ofω=curl u in cylindrical coordinates,for the regularity of axisymmetric weak solutions to the 3D incompressible Navier-Stokes equations...We investigate a sufficient condition,in terms of the azimuthal componentω^(θ)ofω=curl u in cylindrical coordinates,for the regularity of axisymmetric weak solutions to the 3D incompressible Navier-Stokes equations.More precisely,we prove that if■,then the weak solution u is actually a regular solution.Similar regularity criterion still holds in the homogeneous Triebel-Lizorkin spaces.展开更多
基金supported by the National Natural Science Foundation of China(11931010,12226326,12226327)the Key Research Project of Academy for Multidisciplinary Studies,Capital Normal Universitysupported by the Anhui Provincial Natural Science Foundation(2408085QA031).
文摘We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navier-Stokes equations for(ρ,u)through a drag force term n(w−u).We prove the global existence of strong solutions to the coupled system when the initial data are small perturbations of the constant equilibrium state.However,due to the pressureless structure,one can only deal with the density n of the pressureless flow through the transport equation and it is crucial to obtain the exact time-decay rates for the corresponding velocity w of the pressureless flow.To this end,we make use of the spectral analysis,low-high frequency decomposition and time-weighted energy method to deduce the large time behavior of(w,ρ,u)and consequently establish the Lyapunov stability of the density n in Sobolev space.
基金supported by the Key Project of the NSFC(12131010)the NSFC(12271032)+2 种基金supported by the NSFC(12371205)the NSF of Guangdong Province(2025A1515012026)supported by the NSF of Guangdong Province(2024A1515013238)。
文摘In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.
基金supported by the National Natural Science Foundation of China(12371221,12161141004,11831011)the Fundamental Research Funds for the Central Universities and Shanghai Frontiers Science Center of Modern Analysis.
文摘In this paper,we consider the Cauchy problem of the isentropic compressible Navier-Stokes equations with degenerate viscosity and vacuum inℝ,where the viscosity depends on the density in a super-linear power law(i.e.,μ(ρ)=ρ^(δ),δ>1).We first obtain the local existence of the regular solution,then show that the regular solution will blow up in finite time if initial data have an isolated mass group,no matter how small and smooth the initial data are.It is worth mentioning that based on the transport structure of some intrinsic variables,we obtain the L^(∞)bound of the density,which helps to remove the restrictionδ≤γin Li-Pan-Zhu[21]and Huang-Wang-Zhu[13].
文摘本文证明带有临界型阻尼项的Navier-Stokes方程在Lei-Lin-Gevrey空间Xa,σ0(ℝ3)中存在唯一的局部解。文章利用不动点定理和热方程解的有关性质来证明这一主要结论。In this paper, it is proved that the Navier-Stokes equation with critical damping terms has a unique local solution in the Lei-Lin-Gevrey space Xa,σ0(ℝ3). In this paper, the main conclusion is proved by using the fixed point theorem and the related properties of the solution of the heat equation.
基金supported by the Natural Science Foundation of Hunan Province of China(2024JJ5123)supported by the Shandong Provincial Natural Science Foundation(ZR2023MA072,ZR2020MA036)。
文摘The existence and uniqueness of stationary solutions to anisotropic Navier-Stokes equations is investigated by a Galerkin technique in this work.Based on this conclusion,we further explore the exponential stability of weak solutions to stochastic anisotropic NavierStokes equations.We present a relationship among different growth exponents,which is sufficient to guarantee the existence,uniqueness and exponential stability of stationary solutions.
基金Supported by the National Natural Science Foundation of China(12361034)the Natural Science Foundation of Shaanxi Province(2022JM-034)。
文摘We investigate a sufficient condition,in terms of the azimuthal componentω^(θ)ofω=curl u in cylindrical coordinates,for the regularity of axisymmetric weak solutions to the 3D incompressible Navier-Stokes equations.More precisely,we prove that if■,then the weak solution u is actually a regular solution.Similar regularity criterion still holds in the homogeneous Triebel-Lizorkin spaces.
