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arXiv · 1401.2655

Serfati solutions to the 2D Euler equations on exterior domains

David M. Ambrose·James P. Kelliher·Milton C. Lopes Filho·Helena J. Nussenzveig Lopes
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Abstract

We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial data is a bounded divergence-free velocity field having bounded scalar curl. This work completes and extends the ideas outlined by P. Serfati for the same problem in the whole-plane case. With non-decaying vorticity, the Biot-Savart integral does not converge, and thus velocity cannot be reconstructed from vorticity in a straightforward way. The key to circumventing this difficulty is the use of the Serfati identity, which is based on the Biot-Savart integral, but holds in more general settings.

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David M. Ambrose, James P. Kelliher, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes. 2014-01-12. Serfati solutions to the 2D Euler equations on exterior domains. https://arxiv.org/abs/1401.2655

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