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

Abstract

In this paper, we are concerned with global existence and optimal decay rates ofsolutions for the compressible Hall-MHD equations in dimension three.First, we prove the global existence ofstrong solutions by the standard energy method under the conditionthat 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 obtainedif the initial data belong to $L^1$ additionally.Finally, we apply Fourier splitting method bySchonbek [Arch. Rational Mech. Anal. 88 (1985)] to establish optimal decay rates forhigher 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)].