Asymptotic stability of stationary solutions for Hall magnetohydrodynamic equations

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Abstract

In this paper, we consider the large time behavior of the compressible Hall magnetohydrodynamic equations with Coulomb force in \(\mathbb {R}^3\) near the non-constant equilibrium state. We derive the global existence provided that the initial perturbation is sufficiently small. Moreover, under the further assumption that the doping profile is of small variation, we obtain the convergence rates by combining the linear \(L^p\)\(L^q\) decay estimates.

Keywords

Hall MHD equations Stationary solutions Time decay rate Energy method 

Mathematics Subject Classification

35M31 35B35 35B40 35Q60 35Q35 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific ComputingXiamen UniversityXiamenChina

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