Sylvie Benzoni-Gavage (ENS Lyon)
Dongho Chae (Chung-Ang University)
Toshiaki Hishida (Nagoya University)
Paolo Maremonti (University of Campania “Luigi Vanvitelli”)
Milan Pokorny (Charles University of Prague)

Raphaël Danchin (Université Paris-Est Créteil Val-de-Marne)
Reinhard Farwig (TU Darmstadt)
Sarka Necasova (Czech Academy of Sciences)
Jiri Neustupa (Czech Academy of Sciences)

In contrast to the previous meetings, this workshop will mainly focus on “global results” in mathematical fluid mechanics and on the impact of genuinely “nonlocal terms”. By our idea,

• global results will encompass the analysis of asymptotic decay of solutions in space and/or time and of the asymptotic structure, as well as the dynamical systems point of view. We also have in mind the issues of global-in-time regularity and non-uniqueness for the incompressible Navier-Stokes equations, that despite being still open questions, generated a number of exciting new results and approaches.

The second main topic on

​• nonlocal phenomena in fluid mechanics goes far beyond the non-locality of the pressure function of the Stokes equations. As a matter of fact, it is inherent for several types of non-Newtonian fluids as well as active equations like the (surface) quasi-geostrophic equations acting e.g. as a scalar model for 2D/3D Navier-Stokes and for 3D Euler equations. Nonlocal effects are typical for many flow models due to fractional diffusivity or state equations based on Riesz operators. They are also naturally appear in mathematical biology when modeling flocking and aggregation. The conference will bring together 60 – 70 scientists from various branches of mathematical fluid dynamics all over the world, with focus on global and nonlocal phenomena. Young researchers will have a place of honor in the program. We are planning to publish conference proceedings in an international journal as we did for the last four conferences in this series.

• Par phénomènes non locaux,
nous entendons non seulement ceux qui sont générés par la pression dans le système de Stokes, mais également des mécanismes bien plus complexes qui sont inhérents aux fluides non newtoniens, et aux équations de transport actif telle que SQG (l’équation quasi-geostrophic “de surface”). Rappelons que SQG est un modèle scalaire jouet pour la compréhension des équations de Navier-Stokes en dimension deux ou trois, et pour l’équation d’Euler en dimension trois. Les effets non locaux sont également typiques de différents modèles de mécanique des fluides avec diffusion fractionnaire, ou comportant des équations d’état comprenant des opérateurs de Riesz. Ils apparaissent aussi naturellement en math bio pour modéliser les phénomènes de mouvements de foule ou d’agrégation.