Phase mixing, kinetic theory and fluid mechanics

The connections between kinetic theory and fluid mechanics are deeply rooted in the multitude of phenomena that these theories describe. From the classic examples of gas and plasmas dynamics to the recent applications in collective behavior, the multiscale nature of these problems is undoubtedly a fundamental common feature. Kinetic equations are paramount in modeling large systems of interacting particles, and describing their evolution at the mesoscopic level while using fluid models becomes natural at the macroscopic scale.
From a mathematical perspective, a surge of interest in exploring such links has emerged in recent years. As a result, fundamental advances have been made regarding the well-posedness theory of the equations involved (Boltzmann, Navier-Stokes), their rigorous derivation from the underlying many-particle systems (mean-field limits), mixing phenomena and relaxation to equilibria, and hydrodynamic or other macroscopic limits connecting kinetic and fluids models.
There is a clear need for an extended program to disseminate and digest these recent advances. For example, some of the most exciting recent progress has been obtained by combining PDEs techniques, harmonic analysis, calculus of variations, and probability. Our workshop aims to further develop these connections by bringing together experts from each area, including senior and junior researchers, for a combination of introductory lectures, research seminars, and analysis of open problems.