Analysis of Fluids and Related Topics: 3D gravity water waves with vorticity, Dan Ginsberg, Princeton University

Analysis of Fluids and Related Topics
  • Dan Ginsberg
  • Princeton University
  • 3D gravity water waves with vorticity
Oct 3, 2019
4:30 pm
Fine Hall 322

Speaker:  Dan Ginsberg

Abstract:  We prove a long-term regularity result for three-dimensional gravity water waves with small initial data but nonzero initial vorticity. We consider solutions whose vorticity vanishes on the free boundary and use this to derive a system for the evolution of the free boundary which reduces to the Zakharov/Craig-Sulem formulation in the irrotational case. We are able to continue the solution until a time determined by the size of the initial vorticity in such a way that if the vorticity is zero, one recovers a lifespan T ~ ϵ^{−N} where N can be taken arbitrarily large if the initial data is taken to be arbitrarily smooth.