## The Navier-Stokes Equations and Related Topics

**Date:**
29 September - 1 October 2013

**Location: ** Mathematical Institute, University of Oxford

**Event type:**
CRC Workshop

**Organisers: ** Peter Constantin (Princeton), Gregory Seregin (Oxford), Edriss Titi (UC Irvine)

This three-day workshop will bring together world-leading experts in the field of mathematical hydrodynamics to discuss recent developments in and future directions of research in this very active area of applied analysis.

Topics will include the existence, uniqueness and regularity of the Navier-Stokes equations, Euler’s equations and other related hydrodynamics models, as well as numerical aspects. Recent developments in the mathematical study of incompressible fluid models will also be discussed, including, but not limited to:

- progress on regularity of solutions to the Navier-Stokes equations and certain incompressible geophysical and polymeric fluid models
- large-scale numerical simulations that shed some light on conjectured scenarios for the blow-up of solutions of the 3D Euler’s equations
- progress on regularity of quasi-geostrophic equation with critical dissipation exponent
- new approach to “rough solutions” of Euler via convex integration
- the nearly complete solution of the Onsager conjecture about the energy preserving of the solutions to 3d Euler’s equations

The workshop will facilitate an exciting exchange of ideas, with new ideas emerging as a result of the interaction between the participants who have been chosen to represent the broad mathematical analysis community working on various aspects of hydrodynamics.

**Speakers:** Diego Cordoba (ICMAT), Camillo De Lellis (Zürich), Yoshikazu Giga (Tokyo), Thomas Yuizhao Hou (Caltech), Alexander Kiselev (Wisconsin), Nader Masmoudi (NYU), Laure Saint-Raymond (ENS Paris), Vlad Vicol (Princeton), Sijue Wu (Michigan)

This is one of four concurrent workshops held in association with the 2013 Clay Research Conference.