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

DOI: 10.4236/jamp.2018.611203, PP. 2402-2424

Keywords: Compressible Hall-MHD Equations, Global Existence, Optimal Decay Rates, Energy Estimates

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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.

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