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 {R}² R 2 with vorticity in the Hardy space Hᵖ ({R}²) H p (R 2), for any 2/3 2 / 3 p 1.