Abstract: The water wave equation is a nonlinear PDE which models the evolution of the surface of the ocean. In the past two decades, significant progress has been made in the understanding of this equation with results such as local wellposedness for smooth initial data and global wellposedness for small and smooth initial data. Recently there has been some progress in the study of singularities of this equation such as splash, angled crest waves and pinch off in droplet formation. In this talk, I will talk about recent results for angled crest type waves in the presence of surface tension.
Speaker(s): Siddhant Agrawal (University of Michigan)