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

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 $-2 < γ<0$. For the stronger case $-3 \leq γ\leq -2$, which covers in particular the Coulomb case, we get such a global estimate, but in some weighted $L^2$ space and under a smallness assumption on initial data.

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