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Serfati solutions to the 2D Euler equations on exterior domains

2015; Elsevier BV; Volume: 259; Issue: 9 Linguagem: Inglês

10.1016/j.jde.2015.06.001

ISSN

1090-2732

Autores

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

Tópico(s)

Computational Fluid Dynamics and Aerodynamics

Resumo

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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