Related papers: Global regularity for the 2D MHD equations with pa…
In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in $\mathbb{R}^{n}$ for $n=2,\,3$. In comparison with the work of the 3D fractional Navier-Stokes equations obtained…
The magnetohydrodynamics (MHD) problem is most often studied in a framework where Dirichlet type boundary conditions on the velocity field is imposed. In this Note, we study the (MHD) system with pressure boundary condition, together with…
In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics models which are related to Large Eddy Simulation. We first study existence and uniqueness of solutions in the double viscous case. Then, we study existence and…
This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an…
We present a new regularized Oldroyd-B model in three dimensions which satisfies an energy estimate analogous to that of the standard model, and maintains the positive semi-definiteness of the conformation tensor. This results in the unique…
We consider the three-dimensional incompressible magnetohydrodynamics (MHD) equations in a bounded domain with small volume and free moving surface boundary. We establish a priori estimate for solutions with minimal regularity assumptions…
This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the MHD equations have a unique global strong solution around the equilibrium state $(0,\bf{e_1})$ for…
In this paper, we establish the global well-posedness of the incompressible magnetohydrodynamics (MHD) system on $n-$dimensional $(n\geq 2)$ periodic boxes with either no magnetic diffusivity (non-resistive case) or no fluid viscosity…
In this paper we are concerned with the global well-posedness of solutions to magnetohydrodynamics (MHD) boundary layer equations in analytic function spaces. When the initial data is a small perturbation around a selected profile, and such…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
In this paper, we consider the 2D incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion. We establish local existence and uniqueness of solutions for initial data in $H^s$($s\geq 1$). The proof relays…
In this paper, we are concerned with the global well-posedness of a tri-dimensional MHD system with only vertical viscosity in velocity equation for the large axisymmetric initial data. By making good use of the axisymmetric structure of…
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…
We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we…
We consider the electron magnetohydrodynamics (MHD) in the context where the 3D magnetic field depends only on the two horizontal plane variables. In particular, the magnetic field takes the form $B=\nabla\times (a\vec e_z)+b\vec e_z$ with…
In this paper, we study the global existence of classical solutions to the three dimensional incompressible viscous magneto-hydrodynamical system without magnetic diffusion on periodic boxes, i.e., with periodic boundary conditions. We work…
The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in $\mathbb{R}^3$ remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is…
In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magneto-hydrodynamical system with initial data close enough to the equilibrium state, $(e_3,0).$ Compared with the the previous works…
This paper investigates the stabilization effect of a background magnetic vorticity on electrically conducting fluids. By exploring the dissipation nature of the linearized equations, we prove the global existence of smooth solutions to the…
In this article, we show that the magneto-hydrodynamic system (MHD) in $\R^N$ with variable density, variable viscosity and variable conductivity has a local weak solution in the Besov space $\dot B^{\frac{N}{p_1}}_{p_1,1}(\R^N)\times\dot…