On the rate of convergence to equilibrium for the homogeneous Landau equation with soft potentials

Kleber Carrapatoso (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

We investigate in this work the rate of convergence to equilibrium of solutions to the spatially homogeneous Landau equation with soft potentials. Firstly, we prove a polynomial in time convergence using an entropy method with some new a priori estimates. Finally we prove an exponential in time convergence towards the equilibrium with the optimal rate given by the spectral gap of the associated linearized operator, combining new decay estimates for the semigroup generated by the linearized Landau operator in weighted $L^p$-spaces togheter with the polynomial decay described above.

Mots clés: Landau equation; exponential decay; entropy method; spectral gap; hypodissipativity; soft potentials; polynomial decay

Domaines: Equations aux dérivées partielles [math.AP]

Kleber Carrapatoso. On the rate of convergence to equilibrium for the homogeneous Landau equation with soft potentials. Journal de Mathématiques Pures et Appliquées, 2015, 104 (2), pp.276-310. ⟨10.1016/j.matpur.2015.02.008⟩. ⟨hal-00986158v3⟩