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Energy balance for weak solutions of the 2D Incompressible Euler equations.

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TUR - Mathematical aspects of turbulence: where do we stand?

In 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 Lp, p > 1. In this talk we explore an extension of this result to flows subject to external forcing. We seek conditions on the regularity of the forcing to derive the corresponding energy conservation identity.

This talk is part of the Isaac Newton Institute Seminar Series series.

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