Modern Nonlinear PDE Methods in Fluid Dynamics

This LMS-ERSRC summer school aims to give PhD students and other young researchers the opportunity to attend high quality lectures, delivered by leading international experts, on the analysis of PDE in fluid dynamics. Each of the four main lecture courses will illustrate certain aspects related to the mathematical theory of the incompressible Euler equations. Luigi Ambrosio will present the state-of-the-art on a theory according to which minimizing geodesics on the space of measure-preserving maps on a domain may be regarded as weak solutions of the Euler equations. Camillo De Lellis will describe the ideas around an important recent construction of continuous solutions which dissipate energy for the Euler equations. Adrian Constantin will exhibit the global bifurcation theory approach to existence of large-amplitude free-surface steady water waves with vorticity. Georg Weiss will discuss recent methods and applications in the analysis of regularity and behaviour at singularities in free boundaries.

The titles of the four main lecture courses are:

Variational models for incompressible Euler equations (Luigi Ambrosio, Scuola Normale Superiore, Pisa)
Dissipative solutions of the Euler equations (Camillo De Lellis, University of Zürich)
Bifurcation theory in the context of steady water waves (Adrian Constantin, King's College, London)
Analysis of singularities in free-boundary problems (Georg Weiss, Heinrich Heine University, Düsseldorf)