Oberseminar Mathematische Strömungsmechanik

The quantum kinetic BGK equation is a relaxation model of quantum Boltzmann equation describing dynamics of fermion gases. In this presentation, we consider the existence and asymptotic behavior of the fermionic quantum BGK model. More precisely, we establish the existence of unique classical solutions and their exponentially fast stabilization when the initial data starts sufficiently close to a global Fermi-Dirac distribution. There are two main difficulties unobserved in the study of the classical BGK model. First is linearization process of the quantum equilibrium. Secondly, we must verify that the parameters of equilibrium are uniquely determined through a set of nonlinear equations in each iteration step.