Maxwell Institute for Mathematical Sciences




Meeting of the Edinburgh Mathematical Society

at ICMS / Heriot-Watt University



22 January 2016, 4.30 - 5.30pm
ICMS, 15 South College Street, Edinburgh



Laure Saint-Raymond (ENS Paris)
Linear fluid models as scaling limits of interacting system of particles

In his sixth problem, Hilbert asked for an axiomatization of gas dynamics, and he suggested to use the Boltzmann equation as an intermediate description between the (microscopic) atomic dynamics and (macroscopic) fluid models. The main difficulty to achieve this program is to prove the asymptotic decorrelation between the local microscopic interactions, referred to as propagation of chaos, on a time scale much larger than the mean free time. This is indeed the key property to observe some relaxation towards local thermodynamic equilibrium.
This control of the collision process can be obtained in fluctuation regimes. In a joint work with T. Bodineau and I. Gallagher, we have established a long time convergence result to the linearized Boltzmann equation, and eventually derived the acoustic and incompressible Stokes equations in dimension 2. The proof relies crucially on symmetry arguments, combined with a suitable pruning procedure to discard super exponential collision trees.



Tea will be served from 4pm in the Chapterhouse.

A poster is available here.

 

Past events: EMS Meeting at Heriot-Watt 2014 (Martin Hairer)