{"title":"Non-Uniqueness and Energy Dissipation for 2D Euler Equations with Vorticity in Hardy Spaces","authors":"Miriam Buck, Stefano Modena","doi":"10.1007/s00021-024-00860-9","DOIUrl":null,"url":null,"abstract":"<div><p>We construct by convex integration examples of energy dissipating solutions to the 2D Euler equations on <span>\\({\\mathbb {R}}^2\\)</span> with vorticity in the Hardy space <span>\\(H^p({\\mathbb {R}}^2)\\)</span>, for any <span>\\(2/3<p<1\\)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00860-9.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00860-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We construct by convex integration examples of energy dissipating solutions to the 2D Euler equations on \({\mathbb {R}}^2\) with vorticity in the Hardy space \(H^p({\mathbb {R}}^2)\), for any \(2/3<p<1\).
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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