Non-Uniqueness and Energy Dissipation for 2D Euler Equations with Vorticity in Hardy Spaces

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