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Compactness and stability for planar vortex-pairs with prescribed impulse. (English) Zbl 07269183
Summary: 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.
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
76B47 Vortex flows for incompressible inviscid fluids
76E07 Rotation in hydrodynamic stability
49N25 Impulsive optimal control problems
Full Text: DOI
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