Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 3, pp. 625-642.

Nous établissons des estimations a priori pour les solutions de l'équation de Landau non homogène en espace, dans le cas de potentiels faiblement mous, pour toute donnée initiale, sous l'hypothèse que la masse, l'énergie et la densité d'entropie restent contrôlées. Nos estimations ponctuelles ont une décroissance polynomiale par rapport à la variable de vitesse. Nous démontrons également que si la donnée initiale est bornée par une gaussienne, alors cette borne est propagée pour tous les temps positifs.

We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.

DOI : 10.1016/j.anihpc.2017.07.001
Mots-clés : Landau equation, A priori estimates 
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Cameron, Stephen; Silvestre, Luis; Snelson, Stanley. Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 3, pp. 625-642. doi : 10.1016/j.anihpc.2017.07.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2017.07.001/

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