2018/09/20 by Gi-Chan Bae, Bae, Gi-Chan, Seok-Bae Yun +1
Engineering · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #math.AP
paper · pdf · doi:10.48550/arxiv.1809.07790
40 pages
arxiv created 2018/09/20 · arxiv updated 2018/09/24
In this paper, we consider the existence and asymptotic behavior of the fermionic quantum BGK model, which is a relaxation model of the quantum Boltzmann equation for fermions. 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. A key difficulty unobserved in the study of the classical BGK model is that we must verify that the equilibrium parameters is uniquely determined through a set of nonlinear equations in each iteration step.