TITLE:
Decay Rates of the Compressible Hall-MHD Equations for Quantum Plasmas
AUTHORS:
Dan Jin
KEYWORDS:
Compressible Hall-MHD Equations, Global Existence, Optimal Decay Rates, Energy Estimates
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.11,
November
29,
2018
ABSTRACT: In this
paper, we consider the global existence and decay rates of strong solutions to
the three-dimensional compressible quantum Hall-magneto-hydrodynamics equations. By combing the Lp-Lq estimates for the linearized equations and a standard
energy method, the global existence and its convergence rates are obtained in
various norms for the solution to the equilibrium state in the whole space when
the initial perturbation of the stationary solution is small in some Sobolev
norms. More precisely, the decay rates in time of the solution and its first
order derivatives in L2-norm
are obtained when the L1-norm
of the perturbation is bounded.