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.

8 pages

References in corpus (1)

• On a one-dimensional α-patch model with nonlocal drift and fractional dissipation