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arXiv · 1305.3037

Local Existence for the Spatially Homogeneous Boltzmann Equation with Soft Potentials

Yong-Kum Cho
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Abstract

We prove a local-in-time existence and uniqueness theorem for a smooth classical solution to the spatially homogeneous Boltzmann equation with cutoff soft potentials. Our proof is based on a series of bilinear estimates for the integrability and Sobolev regularity of the associated collision operator. While the global-in-time existence is left inconclusive, we give a lower bound of the maximal time of existence and a necessary condition for finite time extinction of existence.

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Yong-Kum Cho. 2015-10-29. Local Existence for the Spatially Homogeneous Boltzmann Equation with Soft Potentials. https://arxiv.org/abs/1305.3037

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