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arXiv · 2206.09636

Moments creation for the inelastic Boltzmann equation for hard potentials without angular cutoff

Jin Woo Jang·Kunlun Qi
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Abstract

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 $(2+κ)$-moment for $κ>0$ and do not assume any entropy bound.

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Jin Woo Jang, Kunlun Qi. 2023-04-13. Moments creation for the inelastic Boltzmann equation for hard potentials without angular cutoff. https://arxiv.org/abs/2206.09636

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