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 γ ∂ttb 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 γ, which shows that the decay rates closely align with that of the MHD system under the same norm, for any fixed γ>0. In this sense, these decay rates are optimal.
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