Diego Cordoba (ICMAT, Madrid)
Finite time singularities in incompressible fluid interfaces
Abstract:
We consider the evolution of an interface generated
between two immiscible, incompressible fluids. Specifically we study the
Surface Quasi-geostrophic equation (a sharp front of cold and hot
air), the Muskat equation (the interface between oil and water in
sand) and the water wave equation (interface between water and
vacuum). For both Muskat and water wave equations we show the
existence of smooth initial data for which the smoothness of the
interface breaks down in finite time.