Volume 3, Issue 3
$L^2$ Stability and Weak-BV Uniqueness for Nonisentropic Euler Equations

Geng Chen & Alexis F. Vasseur

Commun. Math. Anal. Appl., 3 (2024), pp. 450-482.

Published online: 2024-09

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  • Abstract

We prove the $L^2$ stability for weak solutions of non-isentropic Euler equations in one space dimension whose initial data are perturbed from a small BV data under the $L^2$ distance. Using this result, we can show the uniqueness of small BV solutions among a large family of weak solutions.

  • AMS Subject Headings

35L65, 76N15, 35L45, 35B35

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COPYRIGHT: © Global Science Press

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@Article{CMAA-3-450, author = {Chen , Geng and Vasseur , Alexis F.}, title = {$L^2$ Stability and Weak-BV Uniqueness for Nonisentropic Euler Equations}, journal = {Communications in Mathematical Analysis and Applications}, year = {2024}, volume = {3}, number = {3}, pages = {450--482}, abstract = {

We prove the $L^2$ stability for weak solutions of non-isentropic Euler equations in one space dimension whose initial data are perturbed from a small BV data under the $L^2$ distance. Using this result, we can show the uniqueness of small BV solutions among a large family of weak solutions.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2024-0019}, url = {http://global-sci.org/intro/article_detail/cmaa/23384.html} }
TY - JOUR T1 - $L^2$ Stability and Weak-BV Uniqueness for Nonisentropic Euler Equations AU - Chen , Geng AU - Vasseur , Alexis F. JO - Communications in Mathematical Analysis and Applications VL - 3 SP - 450 EP - 482 PY - 2024 DA - 2024/09 SN - 3 DO - http://doi.org/10.4208/cmaa.2024-0019 UR - https://global-sci.org/intro/article_detail/cmaa/23384.html KW - Compressible Euler system, uniqueness, stability, relative entropy, conservation law. AB -

We prove the $L^2$ stability for weak solutions of non-isentropic Euler equations in one space dimension whose initial data are perturbed from a small BV data under the $L^2$ distance. Using this result, we can show the uniqueness of small BV solutions among a large family of weak solutions.

Chen , Geng and Vasseur , Alexis F.. (2024). $L^2$ Stability and Weak-BV Uniqueness for Nonisentropic Euler Equations. Communications in Mathematical Analysis and Applications. 3 (3). 450-482. doi:10.4208/cmaa.2024-0019
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