Energy balance for forced two-dimensional incompressible ideal fluid flow.

Abstract

Cheskidov et al. (2016 Commun. Math. Phys. 348, 129-143. (doi:10.1007/s00220-016-2730-8)) proved that physically realizable weak solutions of the incompressible two-dimensional Euler equations on a torus conserve kinetic energy. Physically realizable weak solutions are those that can be obtained as limits of vanishing viscosity. The key hypothesis was boundedness of the initial vorticity in [Formula: see text], [Formula: see text]. In this work, we extend their result, by adding forcing to the flow. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.