Regularity of the flow map for the gravity-capillary problem

PDE Seminar
Tuesday, November 13, 2012 - 15:05
1 hour (actually 50 minutes)
Skiles 006
University of Pittsburgh
We prove via explicitly constructed initial data that solutionsto the gravity-capillary wave system in R^3 representing a 2d air-waterinterface immediately fail to be C^3 with respect to the initial data ifthe initial (h_0, \psi_0) \in H^{s + 1/2} \times H^s for s<3, where h isthe free surface and \psi is the velocity potential.