Abstract
Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the constraint set comprises the set of all equimeasurable rearrangements of a given function (representing vorticity) that have a prescribed impulse (linear momentum). A form of orbital stability is deduced.
| Original language | English |
|---|---|
| Pages (from-to) | 547-572 |
| Number of pages | 26 |
| Journal | Journal of Differential Equations |
| Volume | 270 |
| Early online date | 15 Sept 2020 |
| DOIs | |
| Publication status | Published - 5 Jan 2021 |
Funding
The author thanks Helena and Milton Lopes for valuable conversations and he is grateful for the hospitality and support of the Thematic Programme on Incompressible Fluid Dynamics held in 2014 at IMPA (Instituto de Matem?tica Pura e Applicada), Rio de Janeiro, where this research was substantially conducted.
Keywords
- Compactness
- Convexity
- Maximiser
- Rearrangements
- Stability
- Vortex
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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