Shallow water waves with vorticity
Talk by Dr. Angel Castro
Speaker invited by: Prof. Dr. Stefan Sauter
Date: 10.04.14 Time: 15.30 - 16.30 Room: Y27H25
In this talk we introduce a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. This new formulation is cast in Eulerian variable, and in finite depth; we shall show that it can be used to provide uniform bounds on the lifespan and on the norms of the solutions in the singular shallow water regime. As an application to these re- sults, we can provide the first rigorous justification of a shallow water model for water waves in presence of vorticity; we will see in particular that a third equation must be added to the standard model to recover the velocity at the surface from the averaged velocity.