Some A priori estimates for the homogeneous Landau equation with soft potentials

Radjesvarane Alexandre (1) , Chunjin Lin (2) , Jie Liao (3)

1 IRENAV - Institut de Recherche de l'Ecole Navale
2 College of Computer and Information Engineering [Hohai]
3 Department of Mathematics

This paper deals with the derivation of some á priori estimates for the homogeneous Landau equation with soft potentials. Using the coercivity of the Landau operator for soft potentials, we prove a global estimate of weak solutions in $L^2$ space without any smallness assumption on the initial data for $ -2\leq \gamma <0$. For the stronger case $ -3 <\gamma < -2$, we get such a global estimate, but in some weighted $L^2$ space and under a smallness assumption on initial data.

Mots clés: 35H10; 76P05; 84C40

Domaines: Equations aux dérivées partielles [math.AP]

Radjesvarane Alexandre, Chunjin Lin, Jie Liao. Some A priori estimates for the homogeneous Landau equation with soft potentials. 2012. ⟨hal-00786128v1⟩