Related papers: Global well-posedness of $z$-weak solutions to the…
In this paper, we consider the initial-boundary value problem to the three-dimensional primitive equations for the oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical…
In this paper, we consider the initial-boundary value problem of the viscous 3D primitive equations for oceanic and atmospheric dynamics with only vertical diffusion in the temperature equation. Local and global well-posedness of strong…
In this paper, we consider the initial-boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation. Global well-posedness of strong solutions are…
In this paper, we consider the initial-boundary value problem of the 3D primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum equations and only horizontal…
In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation. Global…
The 3D-primitive equations with only horizontal viscosity are considered on a cylindrical domain $\Omega=(-h,h) \times G$, $G\subset \mathbb{R}^2$ smooth, with the physical Dirichlet boundary conditions on the sides. Instead of considering…
Global in time well-posedness of $H^2$ solutions and $z$-weak solutions of the 3D Primitive equations in a bounded cylindrical domain is proved. More specifically, uniform in time boundedness and bounded absorbing sets are obtained for both…
In this paper, we consider the initial-boundary value problem of the three-dimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and horizontal diffusivity. We establish the local, in time,…
This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…
We investigate the initial-boundary value problem for one-dimensional compressible, heat-conductive, non-resistive MHD equations of viscous, ideal polytropic fluids in the Lagrangian coordinates. The existence and Lipschitz continuous…
In this paper, the initial-boundary value problem of the 1D full compressible Navier-Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any $H^1$ initial…
In this paper, we consider the initial-boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility…
First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…
In this paper, the initial-boundary value problem to the three-dimensional inhomogeneous, incompressible and heat-conducting Navier-Stokes equations with temperature-depending viscosity coefficient is considered in a bounded domain. The…
In our previous work (arXiv:2510.00812), we have shown the global existence and incompressible limit of weak solutions to the isentropic compressible magnetohydrodynamic equations involving ripped density and large initial energy in the…
In this paper, we investigate the two-dimensional incompressible primitive equations with fractional horizontal dissipation. Specifically, we establish global well-posedness of strong solutions for arbitrarily large initial data when the…
Consider the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, and subject to outer forces. It is shown that this set of equations is globally strongly well-posed…
We study the initial-boundary value problem for 1D compressible MHD equations of viscous non-resistive fluids in the Lagrangian mass coordinates. Based on the estimates of upper and lower bounds of the density, weak solutions are…
Due to the absence of dynamical equation in the vertical momentum component of the primitive equations (PEs) of atmospheric dynamics, the vertical component of the velocity can be recovered only from the information on the other physical…
We establish some conditional uniqueness of weak solutions to the viscous primitive equations, and as an application, we prove the global existence and uniqueness of weak solutions, with the initial data taken as small $L^\infty$…