Water Waves and Related Fluid Models

Date: 28 September - 2 October 2015

Location: Mathematical Institute, University of Oxford

The aim of this workshop is to discuss recent developments in the theory of water waves and related fluid models.  The main topics to be discussed are: local and global regularity, dynamical formation of singularities, and numerical methods.

In the past five years, new methods have emerged in the study of global solutions of quasilinear evolutions, inspired by the advances in semilinear theory.  The basic idea is to combine the classical energy and vector-fields methods with a new ingredient, namely refined analysis of the Duhamel formula using the Fourier transform method.  These new methods led to major progress in understanding the global dynamics of small-data solutions of many physically relevent Quasilinear models in 3 and 2 dimensions, including the construction of the first nontrivial global solutions in several classical water wave models.  At the same time, new methods have been developed to study the dynamics of large-data solutions, and the formation of certain types of interface singularities, such as the so-called splash singularity, wherein a locally smooth interface self-intersects in finite time.  The workshop will survey these recent developments and future research directions.

Speakers: Thomas Alazard (ENS), Peter Constantin (Princeton), Diego Cordoba (ICMAT), Daniel Coutand (Heriot Watt), Charles Fefferman (Princeton), Javier Gomez Serrano (Princeton), Alex Ionescu (Princeton), Alex Kiselev (Rice), David Lannes (Bordeaux), Victor Lie (Purdue), Nader Masmoudi (Courant), Benoit Pausader (Princeton), Fabio Pusateri (Princeton), Gregory Seregin (Oxford), Jalal Shatah (Courant), Steve Shkoller (UC Davis), Chongchun Zeng (Georgia Tech)