ON THE GLOBAL WELL-POSEDNESS AND OPTIMAL LARGE-TIME BEHAVIOR OF STRONG SOLUTION FOR A MULTI-DIMENSIONAL TWO-FLUID PLASMA MODEL*

Abstract

This article is concerned with the Cauchy problem to a multi-dimensional two-fluid plasma model in critical functional framework which is not related to the energy space. When the initial data are close to a stable equilibrium state in the sense of suitable Lp-type Besov norms, the global well-posedness for the multi-dimensional system is shown. As a consequence, one may exhibit the unique global solution for a class of large highly oscillating initial velocities in physical dimensions N =2,3. Furthermore, based on refined time weighted inequalities in the Fourier spaces, we also establish optimal large-time behavior for the constructed global solutions under a mild additional decay assumption involving only the low frequencies of the initial data.