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Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign
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DOI：10.1002/cpa.22038.png)
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Abstract
En 中文
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 Holder 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 turbulence zone is controlled by the local energy inequality and measures the maximal initial dissipation rate in terms of the vortex sheet strength. (c) 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
Keywords:
WEAK SOLUTIONS
ENERGY-DISSIPATION
INCOMPRESSIBLE EULER
ILL-POSEDNESS
EQUATIONS
CONSERVATION
CONVERGENCE
EVOLUTION
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