Global $\dot H^1 \cap \dot H^{-1}$ solutions to a logarithmically regularized 2D Euler equation

Abstract

We construct global $\dot H^1\cap \dot H^{-1}$ solutions to a logarithmically modified 2D Euler vorticity equation. Our main tool is a new logarithm interpolation inequality which exploits the $L^{\infty-}$-conservation of the vorticity.