The Boltzmann equation without angular cutoff. Global existence and full regularity of the Boltzmann equation without angular cutoff. Part I : Maxwellian case and small singularity.
Résumé
The global existence and uniqueness of classical solutions to the Boltzmann equation without angular cut-off is proved under the condition that the initial data is in some Sobolev space. In addition, the solutions thus obtained are shown to be positive and smooth in all variables. One of the key observations is the introduction of a new important norm related to the singularity in the cross section of the collision operator. This norm captures the essential property of the singularity and yields precisely the dissipation description of the linearized collision operator through the celebrated H-theorem.
Origine : Fichiers produits par l'(les) auteur(s)