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A regularity upgrade of pressure
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A regularity upgrade of pressure

Dong Li and Xiaoyi Zhang
ArXiv.org
06/22/2021
DOI: 10.48550/arXiv.2106.11852
url
https://doi.org/10.48550/arXiv.2106.11852View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.
Mathematics - Analysis of PDEs

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