Related papers: Global regularity for solutions of magnetohydrodyn…
In this paper, we consider the global wellposedness of 3-D incompressible magneto-hydrodynamical system with small and smooth initial data. The main difficulty of the proof lies in establishing the global in time $L^1$ estimate for the…
In this work, we study some special properties of smoothness concerning to the initial value problem associated with the Zakharov-Kuznetsov-(ZK) equation in the $n-$ dimensional setting, $n\geq 2.$ It is known that the solutions of the ZK…
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…
The Velocity-Vorticity (VV) formulation of the incompressible Navier-Stokes equations has become popular in recent years, especially in numerical studies, due to its structural advantages. Recently, with L. Rebholz, we introduced a Voigt…
This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay…
Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this…
This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in $\mathbb{R}^d$, $d=2,3$, with initial data $B_0\in H^s(\mathbb{R}^d)$ and $u_0\in…
In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite…
In this paper, we study the 3D axi-symmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the…
We consider a framework for non-ideal magnetohydrodynamics in general relativity, paying particular attention to the physics involved. The discussion highlights the connection between the microphysics (associated with a given equation of…
This paper examines the global (in time) regularity of classical solutions to the 2D incompressible magnetohydrodynamics (MHD) equations with only magnetic diffusion. Here the magnetic diffusion is given by the fractional Laplacian operator…
In this paper, we study the barotropic compressible magnetohydrodynamic equations with the shear viscosity being a positive constant and the bulk one being proportional to a power of the density in a general two-dimensional bounded simply…
It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled…
We study the Cauchy problem for generalized electron magnetohydrodynamics (EMHD). We establish the local existence and uniqueness of solutions in critical Sobolev spaces, as well as global existence and uniqueness for small initial data. In…
We prove long-term regularity of solutions of the one-fluid Euler-Maxwell system in 3 spatial dimensions, in the case of small initial data with nontrivial vorticity.
We revisit the 3D Cauchy problem of compressible heat-conducting magnetohydrodynamic equations with vacuum as far field density. By delicate energy method, we derive global existence and uniqueness of strong solutions provided that…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field.…
In this paper, the three-dimensional primitive equations with magnetic field (PEM) are considered on a thin domain. We showed the global existence and uniqueness (regularity) of strong solutions to the three-dimensional incompressible PEM…
In this paper, we investigate the global regularity to 3-D inhomogeneous incompressible Navier-Stokes system with axisymmetric initial data which does not have swirl component for the initial velocity. We first prove that the $L^\infty$…