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

被引：3

作者：

Bai, Xiang ^{[1
]}

Miao, Qianyun ^{[2
]}

Tan, Changhui ^{[3
]}

Xue, Liutang ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Mathemat Sci, Lab Math & Complex Syst MOE, Beijing 100875, Peoples R China

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[3] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

来源：

NONLINEARITY | 2024年 / 37卷 / 02期

关键词：

Euler-alignment system; fractional diffusion; global well-posedness; critical Besov space; asymptotic behaviour; NAVIER-STOKES EQUATIONS; OPTIMAL DECAY; DYNAMICS; EXISTENCE; REGULARITY; DIFFUSION; MODEL;

D O I：

10.1088/1361-6544/ad140b

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 behaviour and optimal decay estimates of the solutions as t ->infinity .

引用

页数：46

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