Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment

In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreov...

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Published inNonlinearity Vol. 37; no. 6; pp. 65014 - 65040
Main Authors Bai, Xiang, Li, Lin-An, Xu, Xiaojing
Format Journal Article
LanguageEnglish
Published IOP Publishing 03.06.2024
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ISSN0951-7715
1361-6544
DOI10.1088/1361-6544/ad422b

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Abstract In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment.
AbstractList In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment.
Author Bai, Xiang
Xu, Xiaojing
Li, Lin-An
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Snippet In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment....
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SubjectTerms 35B35
35B40
35Q31
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asymptotic stability
compressible Euler system
rarefaction wave
velocity alignment
Title Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment
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