Non-uniqueness and energy dissipation for 2D Euler equations with vorticity in Hardy spaces

Abstract

We construct by convex integration examples of energy dissipating solutions to the 2D Euler equations on ${\mathbb{R}}^2$ with vorticity in the real Hardy space $H^p({\mathbb{R}}^2)$, for any $2/3<p<1$.

34 pages. Only minor errors have been corrected