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

Ricardo J. Alonso, Véronique Bagland, Laurent Desvillettes, Bertrand Lods

In this paper, we present new estimates for the entropy dissipation of the
Landau-Fermi-Dirac equation (with hard or moderately soft potentials) in terms
of a weighted relative Fisher information adapted to this equation. Such
estimates are used for studying the large time behaviour of the equation, as
well 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.