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Article Dans Une Revue Inventiones Mathematicae Année : 2017

Regularity of the Boltzmann equation in convex domains

Résumé

A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical C^1 solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct W^{1,p} solutions for 1 < p < 2 and weighted W^{1,p} solutions for 2 ≤ p ≤∞as well.

Dates et versions

hal-01425843 , version 1 (03-01-2017)

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Yan Guo, Chanwoo Kim, Daniela Tonon, Ariane Trescases. Regularity of the Boltzmann equation in convex domains. Inventiones Mathematicae, 2017, 207 (1), pp.115-290. ⟨10.1007/s00222-016-0670-8⟩. ⟨hal-01425843⟩
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