Sharp time decay rates of H1 weak solutions for the 2D MHD equations with linear damping velocity

Abstract

This study is concerned with the large time decay rates of the H1 weak solutions for the 2D magnetohydrodynamic equations with linear damping velocity. Due to the inconsistencies of the dissipative effects between linear velocity and Laplacian magnetic diffusion, neither the classic Fourier splitting method nor Kato’s method is available directly. By developing an alternative analysis argument together with an iterative process, we give a detailed description on the sharp upper decay rates for the velocity field and for the magnetic field , . Additionally, the optimal lower decay rates of the magnetic field are also presented.