Decay Rates of the Full Compressible Hall-MHD Equations for Quantum Plasmas

Abstract

In this paper, we are concerned with the Cauchy problem of the full compressible Hall-magnetohydrodynamic equations in three-dimensional whole space. By the energy method, global existence of a unique strong solution is established. If further that the L 1-norm of the perturbation is bounded, we prove the decay rates in time of the solution and its first-order derivatives in L 2-norm via some L p-L q estimates by the linearized operator.