Séminaire de EDP - Physique Mathématique

We derive an entropy stable extension of the Navier-Stokes-Fourier equations into the transition regime of rarefied gases. We do this through a variational multiscale reformulation of the closure of conservation equations derived from the Boltzmann equation. Our reformulation subsumes existing methods such as the Chapman-Enskog expansion. We apply the linearized version of this extension to the stationary heat problem and the Poiseuille channel and compare our analytical solutions to asymptotic and numerical solutions of the linearized Boltzmann equation. In both model problems, our solutions compare remarkably well in the transition regime. For some macroscopic variables, this agreement even extends far beyond the transition regime.

Pas de séminaire

In this talk, we are interested in the asymptotic dynamics of a fast rotating incompressible fluid in the regime of vanishing Rossby number. We assume that the fluid moves in a three-dimensional domain with topography (including the possible presence of a land area) and we impose no-slip conditions at the boundary. By proving a "weak implies strong" convergence principle and constructing Ekman layers adapted to the geometry of the domain, we characterise the limit velocity profile and show that it evolves following a linear dynamics.

The talk is based on a joint work with J.-Y. Chemin (Université Claude Bernard Lyon 1) and I. Gallagher (École Normale Supérieure - Paris).

This talk will be a review about recent results concerning the edge states. This concern fluxes that appear at the extremities of isolating materials and they are called "topological isolants" in physics. Several authors propose a model involving a Dirac equation with a vanishing mass on some curve. We will discuss some some aspects of the mathematical analysis for these models and present the open questions.