相关论文: Large time behavior of the solutions to 3D incompr…
In \cite{ChCa}, Califano and Chiuderi conjectured that the energy of incompressible Magnetic hydrodynamical system is dissipated at a rate that is independent of the ohmic resistivity. The goal of this paper is to mathematically justify…
This paper is concerned with the asymptotic behaviors of global strong solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in two-dimensional periodic domains in…
This paper resolves the global regularity problem for the three-dimensional incompressible magnetohydrodynamics (MHD) equations in the upper half-space with slip boundary conditions, in the presence of a background magnetic field. Motivated…
In this paper, we investigative the large time decay and stability to any given global smooth solutions of the $3$D incompressible inhomogeneous MHD systems. We proved that given a solution $(a, u, B)$ of (\ref{mhd_a}), the velocity field…
A main result of this paper establishes the global stability of the 3D MHD equations with mixed partial dissipation near a background magnetic field in the domain $\Omega=\mathbb{T}^2\times\mathbb{R}$ with $\mathbb{T}^2=[0, 1]^2$. More…
We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot…
We revisit the global existence of solutions with some large perturbations to the incompressible, viscous, and non-resistive MHD system in a three-dimensional periodic domain, where the impressed magnetic field satisfies the Diophantine…
Due to the absence of dissipation mechanism to the inviscid compressible systems, it is a challenging problem to prove their global solvability. In this paper, we are concerned with the initial-boundary value problem to the inviscid and…
This paper resolves the global regularity problem for the three-dimensional compressible magnetohydrodynamics (MHD) equations in the three-dimensional whole space, in the presence of a background magnetic field. Motivated by geophysical…
Whether the global well-posedness of strong solutions of $n$-dimensional compressible isentropic magnetohydrodynamic (MHD for short) equations without magnetic diffusion holds true or not remains an challenging open problem, even for the…
In this paper, we obtain the global well-posedness and the asymptotic behavior of solution of non-resistive 2D MHD problem on the half space. We overcome the difficulty of zero spectrum gap by building the relationship between half space…
This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a…
We characterize the $L^2$ decay rate of solutions to the 3D magneto-micropolar system in terms of the decay character of the initial datum. Due to a linear damping term, the micro-rotational field has a faster decay rate. We also address…
In this paper, we are concerned with the compressible viscous magnetohydrodynamic (MHD) system and investigate the large time behavior of strong solutions near constant equilibrium. In the eighties, Umeda, Kawashima and Shizuta initiated…
This paper is concerned with the stability and large-time behavior of 3D incompressible MHD equations with only vertical dissipation near a background magnetic field. By making full use of the dissipation generated by the background…
This paper studies the asymptotic behavior of smooth solutions to the generalized Hall-magneto-hydrodynamics system (1.1) with one single diffusion on the whole space $\mathbb R^3$. We establish that, in the inviscid resistive case, the…
This paper is denoted to the study of dynamical behavior near explicit finite time blowup solutions for three dimensional incompressible Magnetohydrodynamics (MHD) equations. More precisely, we find a family of explicit finite time blowup…
We consider the three-dimensional incompressible MHD system. Any weak solution satisfying a strong energy inequality is $L^2$-asymptotically stable around a Landau solution. Under an additional integrability assumption on the initial…
This paper solves the global conormal regularity problem for the three-dimensional incompressible MHD equations with slip boundary condition near a background magnetic field. Motivated by applications in geophysics, the MHD system…
In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the…