Laure Saint-Raymond: About the Boltzmann-Grad limit
Thursday, November 22th 2012, 4 p.m.
Felix Klein Hörsaal, MI, Augustusplatz 10, 04103 Leipzig
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Laure Saint-Raymond (born August 4, 1975) is a French mathematician.
Saint-Raymond got her doctorate in 2000 at the University of Paris VII. From 2000 to 2002 she was Chargé des Recherches at the CNRS Laboratory for Numerical Analysis at the University of Paris VI, and from 2002 to 2007 professor at the University of Paris VI (Pierre et Marie Curie, Labor Jacques-Louis Lions). She is currently a professor at the Ecole Normale Superieure.
She deals with nonlinear partial differential equations, specifically the Boltzmann equation (and its hydrodynamic limit) and hydrodynamic equations in geophysics, including the Coriolis forces, with applications to climate phenomena at the equator (collaboration with Isabelle Gallagher). In 2004 she proved together with François Golse the context of weak solutions of the Boltzmann equation (for important classes of the core function in the Boltzmann equation) with the Leray solution of the Navier-Stokes equation. Therefore both received the 2006 SIAG/APDE price. In 2003, she proved the convergence of weak solutions of the Boltzmann equation to solutions of the Euler equations imkompressibler liquids.
In 2008 she received the EMS price and the Price of Science of Paris and the 2009 Ruth Lyttle Satter Prize. In 2008 she was an Invited Speaker at the European Congress of Mathematicians in Amsterdam (Some recent results about the sixth problem of Hilbert: hydrodynamic limit of the Boltzmann equation). Furthermore she received the Pius XI. Gold Medal of the Pontifical Academy of Sciences, the Armand Prize of the French Academy of Sciences and the Peccot Price of the College de France.
The goal of this lecture is to present a derivation of the Boltzmann equation starting from the hamiltonian dynamics of particles in the Boltzmann-Grad limit, i.e. when the number of particles N → ∞ and their size ε → 0 with Nε2 = 1. We will especially discuss the origin of irreversibility and the phenomenon of relaxation towards equilibrium, which are apparently paradoxical properties of the limiting dynamics.