Finite-time singularity formation for angle-crested water waves

Source abstract

We show that the water waves system is locally well-posed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. 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 our a priori energy estimates, we show the existence of initial data in these spaces for which the fluid becomes singular in finite time.