Event description
Starting with the pioneering computations of Stokes in 1847, the search for traveling waves in fluid mechanics has always been a fundamental topic, since they can be seen as building blocks for understanding long-time dynamics.
In this talk, I shall discuss recent results concerning the construction of traveling waves in fluid mechanics (for the Euler, Navier–Stokes, and Water Waves equations) by means of Nash–Moser bifurcation techniques, normal form methods, spectral methods, and pseudo-differential operator techniques.
These problems are very challenging small divisors problem due to the quasi-linear nature of the PDEs, typically in dimension greater than two, which leads to strong perturbative effects and significant resonance phenomena.
This conference is funded by the European Research Council (ERC) under the Horizon Europe research and innovation programme (grant agreement No. 101220121 - project: NEW - Nonuniform Ellipticity Widespread).