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Volume 3, Issue 2
Weak-Strong Uniqueness and High-Friction Limit for Euler-Riesz Systems

Nuno J. Alves, José A. Carrillo & Young-Pil Choi

DOI: 10.4208/cmaa.2024-0011

Commun. Math. Anal. Appl., 3 (2024), pp. 266-286.

Published online: 2024-07

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  • Abstract

In this work, we employ the relative energy method to obtain a weak-strong uniqueness principle for a Euler-Riesz system, as well as to establish its convergence in the high-friction limit towards a gradient flow equation. The main technical challenge in our analysis is addressed using a specific case of a Hardy-Littlewood-Sobolev inequality for Riesz potentials.

  • Keywords

Euler-Riesz equations, weak-strong uniqueness, high-friction limit, relative energy method.

  • AMS Subject Headings

35Q31

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-3-266, author = {Alves , Nuno J.Carrillo , José A. and Choi , Young-Pil}, title = {Weak-Strong Uniqueness and High-Friction Limit for Euler-Riesz Systems}, journal = {Communications in Mathematical Analysis and Applications}, year = {2024}, volume = {3}, number = {2}, pages = {266--286}, abstract = {

In this work, we employ the relative energy method to obtain a weak-strong uniqueness principle for a Euler-Riesz system, as well as to establish its convergence in the high-friction limit towards a gradient flow equation. The main technical challenge in our analysis is addressed using a specific case of a Hardy-Littlewood-Sobolev inequality for Riesz potentials.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2024-0011}, url = {http://global-sci.org/intro/article_detail/cmaa/23229.html} }
TY - JOUR T1 - Weak-Strong Uniqueness and High-Friction Limit for Euler-Riesz Systems AU - Alves , Nuno J. AU - Carrillo , José A. AU - Choi , Young-Pil JO - Communications in Mathematical Analysis and Applications VL - 2 SP - 266 EP - 286 PY - 2024 DA - 2024/07 SN - 3 DO - http://doi.org/10.4208/cmaa.2024-0011 UR - https://global-sci.org/intro/article_detail/cmaa/23229.html KW - Euler-Riesz equations, weak-strong uniqueness, high-friction limit, relative energy method. AB -

In this work, we employ the relative energy method to obtain a weak-strong uniqueness principle for a Euler-Riesz system, as well as to establish its convergence in the high-friction limit towards a gradient flow equation. The main technical challenge in our analysis is addressed using a specific case of a Hardy-Littlewood-Sobolev inequality for Riesz potentials.

Alves , Nuno J.Carrillo , José A. and Choi , Young-Pil. (2024). Weak-Strong Uniqueness and High-Friction Limit for Euler-Riesz Systems. Communications in Mathematical Analysis and Applications. 3 (2). 266-286. doi:10.4208/cmaa.2024-0011
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