Energy balance for forced two-dimensional incompressible ideal fluid flow

Abstract

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.

References in corpus (7)

• Onsager's conjecture and anomalous dissipation on domains with boundary
• Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit
• Remarks on high Reynolds numbers hydrodynamics and the inviscid limit
• Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit
• On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity
• Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy
• On the conservation of energy in two-dimensional incompressible flows