Hadamard well-posedness of the gravity water waves equations

Thursday, October 19, 2017 -
1:30pm to 3:00pm
The gravity water waves equations consist of the incompressible Euler equations and an evolution equation for the free boundary of the fluid domain. Assuming the flow is irrotational, Alazard-Burq-Zuily (Invent. Math, 2014) proved that for any initial data in Sobolev space $H^s$, the problem has a unique solution lying in the same space, here s is the smallest index required to ensure that the fluid velocity is spatially Lipschitz. We will discuss the strategy of a proof of the fact that the flow map is continuous in the strong topology of H^s.
Huy Quang Nguyen
Princeton University
Event Location: 
Fine Hall 1001