Moments creation for the inelastic Boltzmann equation for hard potentials without angular cutoff
| Autor: | Jang, Jin Woo, Qi, Kunlun |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper is concerned with the inelastic Boltzmann equation without angular cutoff. We work in the spatially homogeneous case. We establish the global-in-time existence of measure-valued solutions under the generic hard potential long-range interaction on the collision kernel. In addition, we provide a rigorous proof for the creation of polynomial moments of the measure-valued solutions, which is a special property that can only be expected from hard potential collisional cross-sections. The proofs rely crucially on the establishment of a refined Povzner-type inequality for the inelastic Boltzmann equation without angular cutoff. The class of initial data that we require is general in the sense that we only require the boundedness of $(2+\kappa)$-moment for $\kappa>0$ and do not assume any entropy bound. Comment: 32 pages, 1 figure |
| Databáze: | arXiv |
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