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

Xiang Bai; Qianyun Miao; Changhui Tan; Liutang Xue

doi:10.1088/1361-6544/ad140b

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

Xiang Bai, Qianyun Miao^*, Changhui Tan, Liutang Xue

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 behaviour and optimal decay estimates of the solutions as t → ∞ .

Original language	English
Article number	025007
Journal	Nonlinearity
Volume	37
Issue number	2
DOIs	https://doi.org/10.1088/1361-6544/ad140b
Publication status	Published - 1 Feb 2024

Keywords

35B40
35Q31
35R11
76N10
Euler-alignment system
asymptotic behaviour
critical Besov space
fractional diffusion
global well-posedness

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10.1088/1361-6544/ad140b

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

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 behaviour and optimal decay estimates of the solutions as t → ∞ .",

keywords = "35B40, 35Q31, 35R11, 76N10, Euler-alignment system, asymptotic behaviour, critical Besov space, fractional diffusion, global well-posedness",

author = "Xiang Bai and Qianyun Miao and Changhui Tan and Liutang Xue",

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T1 - Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment

AU - Bai, Xiang

AU - Miao, Qianyun

AU - Tan, Changhui

AU - Xue, Liutang

PY - 2024/2/1

Y1 - 2024/2/1

N2 - 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 → ∞ .

AB - 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 → ∞ .

KW - 35B40

KW - 35Q31

KW - 35R11

KW - 76N10

KW - Euler-alignment system

KW - asymptotic behaviour

KW - critical Besov space

KW - fractional diffusion

KW - global well-posedness

UR - http://www.scopus.com/inward/record.url?scp=85182376025&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/ad140b

DO - 10.1088/1361-6544/ad140b

M3 - Article

AN - SCOPUS:85182376025

SN - 0951-7715

VL - 37

JO - Nonlinearity

JF - Nonlinearity

IS - 2

M1 - 025007

ER -

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

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Keywords

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