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arXiv · 2310.05042

Well/Ill-posedness of the Boltzmann Equation with Soft Potential

Xuwen Chen·Shunlin Shen·Zhifei Zhang
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Abstract

We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in $H^{s}$ Sobolev space. We find the well/ill-posedness separation at regularity $s=\frac{d-1}{2}$, strictly $\frac{1}{2}$-derivative higher than the scaling-invariant index $s=\frac{d-2}{2}$, the usually expected separation point.

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Xuwen Chen, Shunlin Shen, Zhifei Zhang. 2023-10-08. Well/Ill-posedness of the Boltzmann Equation with Soft Potential. https://doi.org/10.1007/s00220-024-05157-6

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