Preprint
A regularity upgrade of pressure
ArXiv.org
06/22/2021
DOI: 10.48550/arXiv.2106.11852
Abstract
For the incompressible Euler equations the pressure formally scales as a quadratic function of velocity. We provide several optimal regularity estimates on the pressure by using regularity of velocity in various Sobolev, Besov and Hardy spaces. Our proof exploits the incompressibility condition in an essential way and is deeply connected with the classic Div-Curl lemma which we also generalise as a fractional Leibniz rule in Hardy spaces. To showcase the sharpness of results, we construct a class of counterexamples at several end-points.
Details
- Title: Subtitle
- A regularity upgrade of pressure
- Creators
- Dong Li - Princeton UniversityXiaoyi Zhang - University of Iowa, Mathematics
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arXiv.2106.11852
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 06/22/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984240769502771
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