$C^{0,α}$ boundary regularity for the pressure in weak formulation of the Euler equations

Claude W. Bardos, Edriss S. Titi

Published 2021-07-12Version 1

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 ``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 that of classical solutions.