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Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign
2022
Communications on Pure and Applied Mathematics
We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a simple closed curve in a suitable Hölder space and the vorticity may not have a distinguished sign. Our solutions are obtained by means of convex integration; they are smooth outside a "turbulence" zone which grows linearly in time around the vortex sheet. As a by-product, this approach shows how the growth of the
doi:10.1002/cpa.22038
fatcat:7suzsiqjtbhq7cv6j2fysviu5y