This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equation...This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equations converge to those of zero thermal diffusivity Boussinesq equations as the thermal diffusivity tends to zero,and the convergence rate is established.In addition,we prove that the boundary-layer thickness is of the valueδ(k)=k^(α)with anyα∈(0,1/4)for a small diffusivity coefficient k>0,and we also find a function to describe the properties of the boundary layer.展开更多
this paper,we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion.Firstly,we establish the global regularity for this system with fractional diffusionα=β=5/4.Secondly,by adding only ...this paper,we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion.Firstly,we establish the global regularity for this system with fractional diffusionα=β=5/4.Secondly,by adding only a damp term,we obtain the global well-posedness for small initial data.展开更多
基金the National Natural Science Foundation of China(12061037,11971209)the Natural Science Foundation of Jiangxi Province(20212BAB201016)National Natural Science Foundation of China(11861038)。
文摘This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equations converge to those of zero thermal diffusivity Boussinesq equations as the thermal diffusivity tends to zero,and the convergence rate is established.In addition,we prove that the boundary-layer thickness is of the valueδ(k)=k^(α)with anyα∈(0,1/4)for a small diffusivity coefficient k>0,and we also find a function to describe the properties of the boundary layer.
基金supported by the National Natural Science Foundation of China(No.12101011)Natural Science Foundation of Anhui Province(No.1908085QA05)and the PhD Scientific Research Start-up Foundation of Anhui Normal University(No.751935).J.Li was supported by the National Natural Science Foundation of China(Nos.11801090,12161004),Postdoctoral Science Foundation of China(Nos.2020T130129,2020M672565)and Jiangxi Provincial Natural Science Foundation(No.20212BAB211004).X.Yin was supported by National Natural Science Foundation of China(No.11901005).
文摘this paper,we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion.Firstly,we establish the global regularity for this system with fractional diffusionα=β=5/4.Secondly,by adding only a damp term,we obtain the global well-posedness for small initial data.
