2023/02/28 by Diego Córdoba, Alberto Enciso, Cordoba, Diego +3
Mathematics · Earth and Planetary Sciences · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Ocean Waves and Remote Sensing
paper · pdf · doi:10.48550/arxiv.2303.00027
We show that the water waves system is locally wellposed 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.