C 0, α boundary regularity for the pressure in weak solutions of the 2 d Euler equations-Reference-Cited by-同舟云学术

C ^{0,
α} boundary regularity for the pressure in weak solutions of the 2 d Euler equations

Published:2022-01-17 Issue:2218 Volume:380 Page:
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Bardos Claude W.¹^ORCID,Titi Edriss S.²³⁴

Affiliation:

1. Laboratoire J.-L. Lions, BP187, 75252 Paris Cedex 05, France

2. Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

3. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK

4. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel

Abstract

The purpose of this article is to give a complete proof of a C 0 , α regularity result for the pressure for weak solutions of the two-dimensional ‘incompressible Euler equations’ when the fluid velocity enjoys the same type of regularity in a compact simply connected domain with C 2 boundary. To accomplish our result, we realize that it is compulsory to introduce a new weak formulation for the boundary condition of the pressure, which is consistent with, and equivalent to, that of classical solutions. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2021.0073

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