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.

# Ergodic Theory & Statistical Mechanics

This weekly seminar welcomes many visiting speakers and also provides a forum for results by Princeton/IAS faculty and graduate students. While most talks focus on one of the two namesake topics, there tends to be overlap with other fields. Most recently, talks have included material on celestial mechanics, number theory, probability theory, the Schrodinger equation, spectral theory and Teichmueller theory.

Organizer(s):

For more information about this seminar, contact Yakov Sinai or Jon Fickenscher

**Please note room location is now Fine Hall 1001.**

**Please click on seminar title for complete abstract.**

October 19, 2017

1:30pm - 3:00pm

##### Hadamard well-posedness of the gravity water waves equations

Location

Fine Hall 1001

Speaker: Huy Quang Nguyen,

Princeton University

Princeton University

October 26, 2017

2:00pm - 3:30pm

##### TBA-: Hahng-Yun Chu

Location

Jadwin Hall 111

Speaker: Hahng-Yun Chu,

Chungnam National University & Korea Institute for Advanced Study

Chungnam National University & Korea Institute for Advanced Study

November 30, 2017

11:20am - 11:20am

##### TBA-Joel Moreira

Location

Fine Hall 1001

Speaker: Joel Moreira,

Northwestern University

Northwestern University