C^{0,α} boundary regularity for the pressure in weak formulation of the 2d Euler equations
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Authors
Bardos, Claude W
Titi, Edriss S
Publication Date
2021-07-12Journal Title
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN
1364-503X
Publisher
The Royal Society
Type
Article
This Version
AM
Metadata
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Bardos, C. W., & Titi, E. S. (2021). C^{0,α} boundary regularity for the pressure in weak formulation of the 2d Euler equations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences https://doi.org/10.1098/rsta.2021.0073
Abstract
The purpose of this note 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.
Keywords
math.AP, math.AP, 35Q35, 35Q31, 7603
Identifiers
External DOI: https://doi.org/10.1098/rsta.2021.0073
This record's URL: https://www.repository.cam.ac.uk/handle/1810/331142
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