Decay Rates of the Compressible Hall-MHD Equations for Quantum Plasmas - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.11, November 2018

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

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Download as PDF (Size: 502KB) PP. 2402-2424

DOI: 10.4236/jamp.2018.611203 813 Downloads 1,374 Views Citations

Author(s)

Dan Jin

Affiliation(s)

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

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 L^p-L^q 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.

KEYWORDS

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

Share and Cite:

Jin, D. (2018) Decay Rates of the Compressible Hall-MHD Equations for Quantum Plasmas. Journal of Applied Mathematics and Physics, 6, 2402-2424. doi: 10.4236/jamp.2018.611203.

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