The JEDP 2020 conference has been cancelled. We already invite you for the next edition which will take place in Obernai, Monday June 7th — Friday June 11th 2021.

The « Journées Équations aux Dérivées Partielles » is the annual conference of the CNRS groupement de recherche « Analyse des équations aux dérivées partielles ».

Lecture (6h) : Cancelled

Thierry Gallay (Université Grenoble-Alpes)
« Inviscid damping, enhanced dissipation, and stability threshold »

Abstract: In recent years a tremendous activity has been devoted to the stability analysis of parallel flows in two or three-dimensions, and to related questions concerning two-dimensional vortices. Although the first general results in hydrodynamic stability theory date back to the nineteenth century, the modern developments take advantage of sophisticated mathematical techniques, including dispersive estimates for evolution groups with purely continuous spectrum, pseudospectral or subelliptic estimates for nonselfadjoint operators, and carefully designed space-time norms.

The aim of this series of lectures is to give a self-contained introduction to the recent mathematical literature on hydrodynamic stability theory. To keep the topics within reasonable limits, emphasis will be put on two-dimensional flows in the absence of boundaries. Our goals are threefold:

1) For parallel flows in ideal fluids, to explain how the mixing due to the shear gives rise to linear inviscid damping in Sobolev spaces;

2) For viscous shear flows or vortices, to describe the interaction between advection and diffusion that leads to enhanced dissipation for large Reynolds numbers;

3) In all cases, to determine the stability threshold, namely the size of the perturbations for which the nonlinear evolution can be controlled using the decay properties of the linear semigroup.

The presentation will be complemented by the detailed analysis of classical examples, such as the Couette flow in a two-dimensional channel, the Kolmogorov flow in a two-dimensional torus, and the Lamb-Oseen vortex in the plane. As for the prerequisites, the lectures do not require any deeper knowledge of fluid mechanics than a certain familiarity with the basic equations. However, constant use will be made of standard notions and
results in spectral theory and operator theory.


Invited speakers : Cancelled

Roberta Bianchini (Sorbonne Université)
Roland Donninger (Universität Wien, Autriche)
Mitia Duerinckx (CNRS & Université Paris-Sud)
Sylvain Ervedoza (CNRS & Université de Bordeaux)
Clotilde Fermanian (Université Paris-Est Créteil)
Peter Hintz (MIT, Boston, USA)
Paul Laurain (Université Paris-Diderot)
Eugenia Malinnikova (NTNU, Trondheim, Norvège)
Alexander Mielke (Weierstrass Institute, Berlin, Allemagne)
Vahagn Nersesyan (Université de Versailles)
Galina Perelman (Université Paris-Est Créteil)
Alexander Strohmaier (University of Leeds, Angleterre)
Emil Wiedemann (Universität Ulm, Allemagne)

With the financial support of the CNRS, the Grand Est region and the city of Obernai