Large time behavior of solutions to the 2D damped wave-type magnetohydrodynamic equations

Abstract

In this paper, we are concerned with the 2D damped wave-type magnetohydrodynamic system (abbreviated as MHD-wave system). The purpose of this paper is to study the large time behavior of solutions to the MHD-wave system, espesically to investigate the influence of the bad term ${\hat{I}}^3{\partial }_{tt}b$ on the large time behavior. Rates of decay are obtained for both the solutions and higher derivatives in different Sobolev spaces with explicit rates of ${\hat{I}}^3$, which shows that the decay rates closely align with that of the MHD system under the same norm, for any fixed ${\hat{I}}^3>0$. In this sense, these decay rates are optimal.

39 pages