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. - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

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.

Seiji Ukai
  • Fonction : Auteur
  • PersonId : 856942
Chao-Jiang Xu
  • Fonction : Auteur
  • PersonId : 856943
Tong Yang
  • Fonction : Auteur
  • PersonId : 856944

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.
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Dates et versions

hal-00439227 , version 1 (06-12-2009)
hal-00439227 , version 2 (27-12-2009)
hal-00439227 , version 3 (27-10-2010)

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Radjesvarane Alexandre, Y. Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. 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.. 2009. ⟨hal-00439227v2⟩
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