Equivariant critical point theory and bifurcation of 3d gravity-capillary Stokes waves
Equivariant critical point theory and bifurcation of 3d gravity-capillary Stokes waves
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Massimiliano Berti, SISSA & IAS
Fine Hall 314
We present novel existence results of 3d gravity-capillary periodic traveling waves. In particular we prove the bifurcation of multiple, geometrically distinct truly 3dStokes waves having the same momentum of any non-resonant 2d Stokes wave. This unexpected 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 novel topological arguments based on equivariant Morse-Conley theory. Joint work with T. Barbieri and M. Mazzucchelli.