Hypocoercivity for a linearized multi-species Boltzmann system
Joint work with A. Juengel, C. Mouhot, N. Zamponi.
A new coercivity estimate on the spectral gap of the linearized Boltzmann
collision operator for multiple species is proved. The assumptions on the
collision kernels include hard and Maxwellian potentials with Grad's
condition. Two proofs are given: a non-constructive one, based on the
of the collision operator into a compact and a coercive part, and a
one, which exploits the "cross-effects" coming from collisions between
species and which yields explicit constants.
Based on the spectral-gap estimate, the exponential convergence towards
global equilibrium with explicit rate is shown for solutions to
the linearized multi-species Boltzmann system on the torus.
The convergence is achieved by the interplay between
the dissipative collision operator and the conservative transport term
proved by using the hypocoercivity method of Mouhot and Neumann (2006).