Long time dynamics for the Landau-Fermi-Dirac equation with hard potentials

Abstract

In this document we discuss the long time behaviour for the homogeneous Landau-Fermi-Dirac equation in the hard potential case. Uniform in time estimates for statistical moments and Sobolev regularity are presented and used to prove exponential relaxation of non degenerate distributions to the Fermi-Dirac statistics. All these results are valid for rather general initial datum. An important feature of the estimates is the independence with respect to the quantum parameter. Consequently, in the classical limit the same estimates are recovered for the Landau equation.

References in corpus (2)

• Entropy dissipation estimates for the Landau equation in the Coulomb case and applications
• On the rate of convergence to equilibrium for the homogeneous Landau equation with soft potentials

Cited by in corpus (1)

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