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arXiv · 1907.02483

Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates

Thomas Chen·Ryan Denlinger·Nataša Pavlović
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Abstract

We provide a new analysis of the Boltzmann equation with constant collision kernel in two space dimensions. The scaling-critical Lebesgue space is $L^2_{x,v}$; we prove global well-posedness and a version of scattering, assuming that the data $f_0$ is sufficiently smooth and localized, and the $L^2_{x,v}$ norm of $f_0$ is sufficiently small. The proof relies upon a new scaling-critical bilinear spacetime estimate for the collision "gain" term in Boltzmann's equation, combined with a novel application of the Kaniel-Shinbrot iteration.

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Thomas Chen, Ryan Denlinger, Nataša Pavlović. 2019-07-04. Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates. https://arxiv.org/abs/1907.02483

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