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

DOI10.1098/RSTA.2021.0073arXiv2107.05703MaRDI QIDQ6372613

Publication date: 12 July 2021

Abstract: The purpose of this note is to give a complete proof of a

C^{0, a l p h a}

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.

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Euler equations (35Q31)

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