Optimal convergence rates of the magnetohydrodynamic model for quantum plasmas with potential force

Abstract

In this paper, we consider the quantum magnetohydrodynamic model for quantum plasmas with potential force. We prove the optimal decay rates for the solution to the stationary state in the whole space in the L q − L 2 norm with 1 ≤ q ≤ 2. The proof is based on the optimal decay of the linearized equations, multi-frequency decompositions and nonlinear energy estimates.

Existence and stability of stationary solutions to the compressible quantum model

“…For the time decay rates for the compressible quantum Hall-magnetohydrodynamic model, one can refer to [24]. When the external force is considered, Xu and Pu [26] proved the optimal convergence rates of the magnetohydrodynamic model for quantum plasmas with potential force.…”