New estimates for the entropy dissipation of the Landau-Fermi-Dirac equation

About the use of entropy production for the Landau-Fermi-Dirac equation

We present new estimates for the entropy dissipation of the landau-fermi-dirac equation (with hard or moderately soft potentials) in termsof a weighted relative fisher information adapted to this equation.Such estimates are used for studying the large time behaviour of the equation, aswell as for providing new a priori estimates (in the soft potential case).An important feature of such estimates is that they are uniform with respect to the quantum parameter.Consequently, the same estimations are recovered for the classical limit, that is the landau equation.