In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of on...In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of one of its directions(x,y)are assumed to be L^(2)(R^(2)).Our results only need the lower regularity of the initial data,which ensures the uniqueness of the solutions.展开更多
In this paper,we investigate the vanishing viscosity limit problem for the 3-dimensional(3D)incompressible Navier-Stokes equations in a general bounded smooth domain of R^3 with the generalized Navier-slip boundary co...In this paper,we investigate the vanishing viscosity limit problem for the 3-dimensional(3D)incompressible Navier-Stokes equations in a general bounded smooth domain of R^3 with the generalized Navier-slip boundary conditions u^ε·n=0,n×(ω^ε)=[Bu^ε]τon∂Ω.Some uniform estimates on rates of convergence in C([0,T],L2(Ω))and C([0,T],H^1(Ω))of the solutions to the corresponding solutions of the ideal Euler equations with the standard slip boundary condition are obtained.展开更多
In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded domains.On the boundary,the veloci...In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded domains.On the boundary,the velocity field fulfills a Navier-slip condition,while the magnetic field satisfies the insulating condition.It is shown that the initial boundary value problem has a global weak solution for a general smooth domain.More importantly,for a flat domain,we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.展开更多
基金partially supported by key research grant of the Academy for Multidisciplinary Studies,CNUsupported by NSFC(11901040)+1 种基金Beijing Municipal Commission of Education(KM202011232020)Beijing Natural Science Foundation(1204030)。
文摘In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of one of its directions(x,y)are assumed to be L^(2)(R^(2)).Our results only need the lower regularity of the initial data,which ensures the uniqueness of the solutions.
基金This research is supported in part by NSFC 10971174,and Zheng Ge Ru Foundation,and Hong Kong RGC Earmarked Research Grants CUHK-4041/11P,CUHK-4042/08P,a Focus Area Grant from the Chinese University of Hong Kong,and a grant from Croucher Foundation.
文摘In this paper,we investigate the vanishing viscosity limit problem for the 3-dimensional(3D)incompressible Navier-Stokes equations in a general bounded smooth domain of R^3 with the generalized Navier-slip boundary conditions u^ε·n=0,n×(ω^ε)=[Bu^ε]τon∂Ω.Some uniform estimates on rates of convergence in C([0,T],L2(Ω))and C([0,T],H^1(Ω))of the solutions to the corresponding solutions of the ideal Euler equations with the standard slip boundary condition are obtained.
基金supported by National Natural Science Foundation of China(Grant No.11771300)supported by National Natural Science Foundation of China(Grant No.11871412)+2 种基金National Science Foundation of Guangdong(Grant No.2020A1515010554)supported by Zheng Ge Ru Foundation,Hong Kong Research Grants Council Earmarked Research(Grant Nos.CUHK14302819,CUHK14300917 and CUHK14302917)Basic and Applied Basic Research Foundation of Guangdong Province(Grant No.2020B1515310002)。
文摘In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded domains.On the boundary,the velocity field fulfills a Navier-slip condition,while the magnetic field satisfies the insulating condition.It is shown that the initial boundary value problem has a global weak solution for a general smooth domain.More importantly,for a flat domain,we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.