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Pré-Publication, Document De Travail Année : 2012

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

Jie Liao
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Résumé

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 < \gamma <0$. For the stronger case $ -3 \leq \gamma \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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Dates et versions

hal-00786128 , version 1 (07-02-2013)
hal-00786128 , version 2 (08-02-2013)
hal-00786128 , version 3 (30-03-2013)

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Radjesvarane Alexandre, Jie Liao, Chunjin Lin. Some A priori estimates for the homogeneous Landau equation with soft potentials. 2012. ⟨hal-00786128v3⟩
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