Large-time behavior of the strong solution to nonhomogeneous incompressible MHD system with general initial data

Shengquan Liu

doi:10.1186/s13661-015-0471-9

Abstract

This paper investigates the large-time behavior of strong solutions to the nonhomogeneous incompressible magnetohydrodynamic equations on a bounded domain in $\mathbb{R}^{2}$ . Based on uniform estimates, we prove that the velocity, the magnetic field, and their derivatives converge to zero in $L^{2}$ norm as time goes to infinity without any additional assumption on the initial data and external force by a pure energy method.

Highlights

Magnetohydrodynamics (MHD) studies the theory of the macroscopic interaction of electrically conducting fluids with a magnetic field
In [ ], the authors considered the asymptotic behavior of the strong solutions to MHD equations in a half space
The main purpose of this paper is to investigate the influence of the magnetic fields, viscosity, and boundary effects on the behavior of the solution of ( . )-( . )

Summary

Introduction

Magnetohydrodynamics (MHD) studies the theory of the macroscopic interaction of electrically conducting fluids with a magnetic field. ), Huang and Wang [ ] recently proved the unique global strong solution with initial vacuum in dimension two without external force f. For Cauchy problem, the authors in [ ] studied the long time behavior of solutions to the MHD equations in two and three dimensions with some smallness conditions. In [ ], the authors considered the asymptotic behavior of the strong solutions to MHD equations in a half space.

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