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arXiv · 2206.11931

Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel

Xuwen Chen·Justin Holmer
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Abstract

We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, which are neither near equilibrium nor self-similar, to the equation, and prove that the well/ill-posedness threshold in $H^{s}$ Sobolev space is exactly at regularity $s=1$, despite the fact that the equation is scale invariant at $s=\frac{1}{2}$.

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Xuwen Chen, Justin Holmer. 2022-06-23. Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel. https://doi.org/10.1007/s40818-024-00177-w

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