Workshop: Finite-time singularity formation for angled-crested water waves, Alberto Enciso

Date: 2023-09-11

Time: 11:00 - 11:50


Alberto Enciso, ICMAT


We shall see that the water waves system is locally wellposed in a class of weighted Sobolev spaces that allows for interfaces with corners. These singular points are not rigid: if the initial interface exhibits a corner, it remains a corner but generically its angle changes. Using a characterization of the asymptotic behavior of the fluid near a corner that follows from the a priori energy estimates, we shall show that there are initial data in these spaces (possibly smooth but at a unique corner point) for which the fluid becomes singular in finite time.

The talk is based one joint work with Diego Córdoba and Nastasia Grubic.