{"title":"Energy Equality Criteria in the Navier–Stokes Equations Involving the Pressure","authors":"Yanqing Wang, Jiaqi Yang, Yulin Ye","doi":"10.1007/s00021-025-00917-3","DOIUrl":null,"url":null,"abstract":"<div><p>Very recently, Barker (Proc. Amer. Math. Soc. Ser. B 11: 436-451, 2024), Barker and Wang (J Differ Equ 365:379–407, 2023), and, Beirao da Veiga and Yang (J. Geom. Anal. 35: no. 1, Paper No. 15, 14 pp, 2025) applied the higher integrability of weak solutions to study the singular set and energy equality of weak solutions to the incompressible Navier–Stokes equations with supercritical assumptions, respectively. In the spirit of this and, Leslie and Shvydkoy’s work (SIAM J Math Anal 50:870–890, 2018), we present some energy equality criteria for suitable weak solutions up to the first potential blow-up time in terms of pressure, its gradient or the direction of the velocity by <span>\\(L^{p}\\)</span> bound of the incompressible Navier–Stokes equations. Furthermore, along the same lines, we establish some <span>\\(L^{p}\\)</span> estimate of the isentropic compressible Navier–Stokes equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-025-00917-3","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
Very recently, Barker (Proc. Amer. Math. Soc. Ser. B 11: 436-451, 2024), Barker and Wang (J Differ Equ 365:379–407, 2023), and, Beirao da Veiga and Yang (J. Geom. Anal. 35: no. 1, Paper No. 15, 14 pp, 2025) applied the higher integrability of weak solutions to study the singular set and energy equality of weak solutions to the incompressible Navier–Stokes equations with supercritical assumptions, respectively. In the spirit of this and, Leslie and Shvydkoy’s work (SIAM J Math Anal 50:870–890, 2018), we present some energy equality criteria for suitable weak solutions up to the first potential blow-up time in terms of pressure, its gradient or the direction of the velocity by \(L^{p}\) bound of the incompressible Navier–Stokes equations. Furthermore, along the same lines, we establish some \(L^{p}\) estimate of the isentropic compressible Navier–Stokes equations.
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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