Sharp Global Well-Posedness for the Logarithmically Regularized 2D Euler Equations

Abstract

We consider solutions to the two-dimensional Euler equations with a logarithmically regularized velocity given by $u={\nabla }^{\perp }(-\Delta {)}^{-1}{\ln }^{-\gamma }(|\nabla |+e)\omega$ and initial vorticity in ${\dot{H}}^1\cap {\dot{H}}^{-1}({\mathbb{R}}^2)$. We show that if $\gamma >1/2$, then global well-posedness holds.

arXiv commentFixed minor typographical errors