Hadamard wellposedness of the gravity water waves equations
Hadamard wellposedness of the gravity water waves equations

uy Quang Nguyen, Princeton University
Fine Hall 1001
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, AlazardBurqZuily (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.