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Energy balance for forced two-dimensional incompressible ideal fluid flow

In [Commun Math Phys 348(1), 129-143, 2016], Cheskidov et al. proved that physically realizable weak solutions of the incompressible 2D 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 $L^p$, $p>1$. In this work we extend their result, by adding forcing to the flow.