Hypocoercivty in cascade for linearized Boltzmann type equations with external potentials
In this talk we present a very recent results on the return to the equilibrium
for inhomogeneous linearized kinetic equations when the collision kernel has 5 conserved moments
(mass, momentum and energy). We study the case when there is an external potential acting on the system of particles.
When there is no axisymetry of harmonicity of the potentiel, there is a unique equilibrium state (for a given initial mass and energy), and
the return to the equilibrium is the result of a cascade of hypocoercive and damping effects. When there are some axisymmetries or harmonicity of the potential, special solutions appear. We shall try to explain
the general scheme of the proof and the main mathematical and physical ideas behind.
This a joint work with K. Carrapatoso, J. Dolbeault, S. Mischler, C. Schmeiser and C. Mouhot.