The APDE seminar on Monday, 05/11, will be given by Albert Ai online via Zoom from 4:10 to 5pm. To participate, email Georgios Moschidis (email@example.com) or Thibault de Poyferré (firstname.lastname@example.org).
Title: Two dimensional gravity waves at low regularity.
Abstract: In this talk, we will consider the low regularity well-posedness problem for the two dimensional gravity water waves. This quasilinear dispersive system admits an interesting structure which we exploit to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier energy estimates of Hunter-Ifrim-Tataru. These results allow us to significantly lower the regularity threshold for local well-posedness, even without using dispersive properties. This is joint work with Mihaela Ifrim and Daniel Tataru.