Global weak solutions and long time behavior for 1D compressible MHD equations without resistivity

摘要

We study the initial-boundary value problem for 1D compressible MHD equationsof viscous non-resistive fluids in the Lagrangian mass coordinates. Based onthe estimates of upper and lower bounds of the density, weak solutions areconstructed by approximation of global regular solutions, the existence ofwhich has recently been obtained by Jiang and Zhang in [17]. Uniqueness of weaksolutions is also proved as a consequence of Lipschitz continuous dependence onthe initial data. Furthermore, long time behavior for global solutions isinvestigated. Specifically, based on the uniform-in-time bounds of the densityfrom above and below away from zero, together with the structure of theequations, we show the exponential decay rate in L^2- and H^1-normrespectively, with initial data of arbitrarily large.