Decay rates of the magnetohydrodynamic model for quantum plasmas

Abstract

In this paper, we consider the quantum magnetohydrodynamic model for quantum plasmas. We prove the optimal decay rates for the solution to the constant state in the whole space in the $$L^{p}$$ -norm with $$2\le p\le 6$$ and its first derivatives in $$L^{2}$$ -norm. The proof is based on the optimal decay of the linearized equation and nonlinear energy estimates.