2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

Fluid Approximations of the Linearized Granular Gases Operator

Thomas Rey

University of Maryland

In this talk, we are interested in the spectral study of the granular gases operator with a thermal bath, in a space homogeneous setting, linearized around an homogeneous equilibrium. We will perform a study inspired from the classical paper of R. Ellis and M. Pinsky about the spectrum of the linearized Boltzmann operator, The big difference being that we will consider a Banach $L^1$ setting instead of the classical $L^2$ one. We will first give a localization of the spectrum, and then an expansion of the branches of eigenvalues of this operator, for small Fourier (in space) frequencies and small inelasticity. This is a work in progress.