## 2012 Young Researchers Workshop:Kinetic Description of Multiscale Phenomena

### Fluid Approximations of the Linearized Granular Gases Operator

Thomas Rey

University of Maryland

Abstract:

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.