Seminario di Analisi Matematica

Giovedì 9 aprile alle ore 14:00, Massimiliano Berti (SISSA-Trieste) terrà un Seminario di Analisi Matematica dal titolo "Equivariant critical point theory and bifurcation of 3d gravity-capillary Stokes waves".

Abstract: We establish novel existence and multiplicity results for 3d gravity-capillary periodic Stokes waves -traveling water wave solutions that are steady in a moving frame- with an arbitrary lattice spatial period. Surprisingly, bifurcation of multiple, geometrically distinct truly 3d Stokes wave orbits emerges in the proximity of any non-resonant 2d Stokes wave. This clustering phenomenon of Stokes waves, observed in physical fluids, is a fundamental consequence of the Hamiltonian nature of the water waves equations, their symmetry groups, and purely topological reasons. Our results are obtained through a variational Lyapunov-Schmidt reduction with Morse-Conley theoretic arguments for a functional defined on a singular topological space invariant under a 2-torus action. The Lyapunov-Schmidt reduction becomes singular in the vicinity of the hyperplanes filled by 2d-waves.
To overcome this, we exhaustively exploit the underlying symmetry groups, providing the complete bifurcation picture of 3d-gravity-capillary periodic Stokes waves.
This is work with T. Barbieri and M. Mazzucchelli.

Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, Via della Vasca Navale 84, aula B.