In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing v...In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing viscosity limit result.展开更多
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes...In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.展开更多
The goal of this article is to study the boundary layer of Navier-Stokes/Allen- Cahn system in a channel at small viscosity. We prove that there exists a boundary layer at the outlet （down-wind） of thickness v, wher...The goal of this article is to study the boundary layer of Navier-Stokes/Allen- Cahn system in a channel at small viscosity. We prove that there exists a boundary layer at the outlet （down-wind） of thickness v, where v is the kinematic viscosity. The convergence in L2 of the solutions of the Navier-Stokes/Allen-Cahn equations to that of the Euler/Allen-Cahn equations at the vanishing viscosity was established. In two dimensional case we are able to derive the physically relevant uniform in space and time estimates, which is derived by the idea of better control on the tangential derivative and the use of an anisotropic Sobolve imbedding.展开更多
基金The authors were partially supported by the National Natural Science Foundation of China （No.11371042）.
文摘In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing viscosity limit result.
基金Supported by the Youth Science Fund for Disaster Prevention and Reduction(201207)Supported by the Teachers’Scientific Research Fund of China Earthquake Administration(20140109)
文摘In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.
文摘The goal of this article is to study the boundary layer of Navier-Stokes/Allen- Cahn system in a channel at small viscosity. We prove that there exists a boundary layer at the outlet （down-wind） of thickness v, where v is the kinematic viscosity. The convergence in L2 of the solutions of the Navier-Stokes/Allen-Cahn equations to that of the Euler/Allen-Cahn equations at the vanishing viscosity was established. In two dimensional case we are able to derive the physically relevant uniform in space and time estimates, which is derived by the idea of better control on the tangential derivative and the use of an anisotropic Sobolve imbedding.
