In this
paper, we consider the global existence and decay rates of strong solutions to
the three-dimensional compressible quantumHall-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.
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