Turning waves and breakdown for incompressible flows
Diego Córdoba,
(Instituto de Ciencias Matemáticas - CSIC Madrid)
Jueves 14 de abril 2011
We consider the evolution of an interface generated between two immiscible
incompressible and irrotational fluids. Specifically we study the Muskat and water wave problems.
We show that starting with a family of initial data given by (x, f(x)), the interface reaches a
regime in finite time in which is no longer a graph. In particular, for the Muskat problem, this result
allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the
solution breaks down.