Communications in Mathematical Sciences

Volume 21 (2023)

Number 4

On the global well-posedness and optimal large-time behavior of strong solution for a multi-dimensional two-fluid plasma model

Pages: 1019 – 1054

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n4.a6

Authors

Fuyi Xu (School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong, China)

Ningning Gao (School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong, China)

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 $L^p$-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.

Keywords

bipolar compressible Navier–Stokes–Poisson system, global well-posedness, optimal large-time behavior, $L^p$-type critical Besov spaces

2010 Mathematics Subject Classification

35Q35, 76W05

Full Text (PDF format)

Received 9 November 2021

Accepted 7 September 2022

Published 24 March 2023