Global existence and optimal decay rates of solutions for compressible Hall-MHD equations

Jincheng  Gao; Zheng-An  Yao

doi:10.3934/dcds.2016.36.3077

Article Contents

2016, Volume 36, Issue 6: 3077-3106. Doi: 10.3934/dcds.2016.36.3077

This issue Previous Article Bubbling on boundary submanifolds for a semilinear Neumann problem near high critical exponents Next Article From the highly compressible Navier-Stokes equations to the porous medium equation -- rate of convergence

Global existence and optimal decay rates of solutions for compressible Hall-MHD equations

Jincheng Gao^1, and
Zheng-An Yao^1,

1.
School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275

Received: April 2015

Revised: October 2015

Published: May 2017

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Abstract

In this paper, we are concerned with global existence and optimal decay rates of solutions for the compressible Hall-MHD equations in dimension three. First, we prove the global existence of strong solutions by the standard energy method under the condition that the initial data are close to the constant equilibrium state in $H^2$-framework. Second, optimal decay rates of strong solutions in $L^2$-norm are obtained if the initial data belong to $L^1$ additionally. Finally, we apply Fourier splitting method by Schonbek [Arch. Rational Mech. Anal. 88 (1985)] to establish optimal decay rates for higher order spatial derivatives of classical solutions in $H^3$-framework, which improves the work of Fan et al.[Nonlinear Anal. Real World Appl. 22 (2015)].

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Mathematics Subject Classification: Primary: 76W05; Secondary: 35A01, 35D35, 74H40.

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