Research
Wednesday, 06 July 2022 20:44

## Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment

Xiang Bai, Qianyun Miao, Changhui Tan and Liutang Xue

Abstract

In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in critical Besov spaces to the considered system with small initial data. The local-in-time solvability is also addressed. Moreover, we show the large-time asymptotic behavior and optimal decay estimates of the solutions as $$t\to\infty$$.

 This work is supported by NSF grant DMS #1853001 and DMS #2108264

arXiv Preprint 2207.02429.