Speaker: Laure Saint-Raymond, Professor of Mathematics at Pierre and Marie Curie University (Paris VI) and École Normale Supérieure
A series of three lectures entitled From Particle Systems to Kinetic Equations.
Lecture III: The case of fluctuations around a global equilibrium
To improve the convergence time, the idea is therefore to consider situations where one can obtain global a priori bounds. Since the system of particles is Hamiltonian, the Gibbs measures are invariant under the flow and provide constant solutions to the Boltzmann equation. By perturbation, we get initial data leading to linear kinetic equations. In the third lecture, we will show that, for such initial data, we can control a priori the collision rate, and extend Lanford's strategy to get a quasi-global convergence result in the low density limit.