Journal article
Serfati solutions to the 2D Euler equations on exterior domains
Journal of Differential Equations, v 259(9), pp 4509-4560
05 Nov 2015
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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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Details
- Title
- Serfati solutions to the 2D Euler equations on exterior domains
- Creators
- David M. Ambrose - Drexel UniversityJames P. Kelliher - University of California, RiversideMilton C. Lopes Filho - Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, BrazilHelena J. Nussenzveig Lopes - Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brazil
- Publication Details
- Journal of Differential Equations, v 259(9), pp 4509-4560
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000359507800003
- Scopus ID
- 2-s2.0-84938200830
- Other Identifier
- 991019168443404721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics