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

Abstract

The purpose of this note is to give a complete proof of a $C^{0,\alpha }$ 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.

References in corpus (1)

• Onsager's Conjecture for the Incompressible Euler Equations in Bounded Domains

Cited by in corpus (4)

• Onsager's Conjecture for Subgrid Scale $\alpha$-Models of Turbulence
• On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains
• Full double Hölder regularity of the pressure in bounded domains
• Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains