Schiffer-type problems and nonradial stationary Euler flows with compact support

Enciso, Alberto

Journées équations aux dérivées partielles (2024), Exposé no. 4, 10 p.

We review some recent results on the existence of nonradial stationary planar Euler flows with compact support. The approach we take relies on an elliptic overdetermined problem motivated by Schiffer’s conjecture in spectral geometry.

Nous passons en revue quelques résultats récents sur l’existence d’écoulements d’Euler stationnaires non radiaux à support compact dans le plan. L’approche que nous adoptons repose sur un problème elliptique surdéterminé, inspiré par la conjecture de Schiffer en géométrie spectrale.

Classification : 35N25, 35Q31, 35B32
Keywords: Eigenvalue problems, radial symmetry, Euler equations
Mots-clés : Problèmes aux valeurs propres, symétrie radiale, équations d’Euler

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