Existence of smooth solutions to the Landau–Fermi–Dirac equation with Coulomb potential

In this paper we prove global-in-time existence of smooth solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb potential. The initial conditions are nonnegative, bounded and integrable. We also show that any weak solution converges, as time grows, towards steady state given by Fermi-Dirac equilibrium distribution. Furthermore, convergence is exponential, provided datum close in a suitable weighted Lebesgue norm.