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C0,α boundary regularity for the pressure in weak solutions of the 2d Euler equations.

Accepted version
Peer-reviewed

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Type

Article

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Authors

Titi, Edriss S 

Abstract

The purpose of this article is to give a complete proof of a [Formula: see text] 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 [Formula: see text] 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)'.

Description

Keywords

Euler equations, boundary effects, pressure regularity

Journal Title

Philos Trans A Math Phys Eng Sci

Conference Name

Journal ISSN

1364-503X
1471-2962

Volume Title

380

Publisher

The Royal Society