| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Bath, Sch Math Sci, Bath BA2 7AY, Avon - England
[2] Univ Fed Rio de Janeiro, Inst Matemat, Ilha Fundao, BR-21941909 Rio De Janeiro, RJ - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Communications in Mathematical Physics; v. 324, n. 2, p. 445-463, DEC 2013. |
| Web of Science Citations: | 2 |
| Abstract | |
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies. (AU) | |
| FAPESP's process: | 06/51079-2 - Geoffrey Robert Burton | University of Bath - Inglaterra |
| Grantee: | Helena Judith Nussenzveig Lopes |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 07/51490-7 - Mathematical aspects of incompressible fluid dynamics |
| Grantee: | Milton da Costa Lopes Filho |
| Support Opportunities: | Research Projects - Thematic Grants |