Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials

This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials . We prove an exponential in time convergence towards the equilibrium, improving results of Desvillettes and Villani. Our approach is based on new spectral gap estimates for the linearized Landau operator in weighted (polynomial or stretched exponential) $L^p$-spaces.no