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Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials

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arxiv 2312.11079 v1 pith:CKMSXKQC submitted 2023-12-18 math.AP

François Golse (CMLS) , Cyril Imbert (DMA) , Luis Silvestre This is my paper · ORCID
classification math.AP
keywords boltzmannequationgammapotentialssoftveryconstructeddimension
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abstract

We prove that the set of singular times for weak solutions of the homogeneous Boltzmann equation with very soft potentials constructed as in Villani (1998) has Hausdorff dimension at most $\frac{|\gamma+2s|}{2s}$ with $\gamma \in [-4s,-2s)$ and $s \in (0,1)$.

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  1. Fisher Information in Kinetic Theory

    math.AP 2025-01 conditional novelty 4.0 of 10

    Fisher information is nonincreasing along the spatially homogeneous Boltzmann equation for all physically relevant collision kernels, yielding regularity for very soft potentials.

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