About the Landau-Fermi-Dirac Equation With Moderately Soft Potentials

We present in this document some essential properties of solutions to the homogeneous Landau-Fermi-Dirac equation for moderately soft potentials. Uniform time estimates statistical moments, $L^{p}$-norm generation and Sobolev regularity are shown using a combination techniques that include recent developments concerning level set analysis spirit De Giorgi refined entropy-entropy dissipation functional inequalities Landau collision operator which extended case question here. As consequence analysis, we prove algebraic relaxation non degenerate distributions towards Fermi-Dirac statistics under weak saturation condition initial datum. All quantitative uniform with respect quantum parameter. They therefore also hold classical limit, is equation.