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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
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
Received 9 November 2021
Accepted 7 September 2022
Published 24 March 2023