Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equation II. Non cuttof case and non maxwellian molecules

Radjesvarane Alexandre (1) , Mouhamad El Safadi (2)

1 Département de Mathématiques (Evry)
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We use Littlewood-Paley theory for the analysis of regularization properties of weak solutions of the homogeneous Boltzmann equation. For non cutoff and non Maxwellian molecules, we show that such solutions are smoother than the initial data. In particular, our method applies to any weak solution, though we assume that it belongs to a weighted L^2 space.

Mots clés: non cutoff collision cross sections; Boltzmann equation; Littlewood-Paley theory; Maxwellian molecules; non cutoff collision cross sections.

Domaines: Equations aux dérivées partielles [math.AP]

Radjesvarane Alexandre, Mouhamad El Safadi. Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equation II. Non cuttof case and non maxwellian molecules. 2007. ⟨hal-00137729⟩