$C^{0,α}$ boundary regularity for the pressure in weak solutions of the $2d$ Euler equations Academic Article uri icon


  • 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.

author list (cited authors)

  • Bardos, C. W., & Titi, E. S.

complete list of authors

  • Bardos, Claude W||Titi, Edriss S

publication date

  • July 2021