Local Existence for the Spatially Homogeneous Boltzmann Equation with Soft Potentials

2013/05/14 by Cho, Yong-Kum
#35Q82 #47G20 #76P05 #82B40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1305.3037

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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