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arXiv · 2501.14697

$l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation

Xuwen Chen·Shunlin Shen·Zhifei Zhang
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Abstract

We broaden the application of the $l^{2}$-decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the $\mathbb{T}^d$ setting. We establish space-time bilinear estimates, and hence the unconditional uniqueness of solutions to the $\mathbb{R}^d$ and $\mathbb{T}^d$ Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff, adopting a unified hierarchy scheme originally developed for the nonlinear Schr\"{o}dinger equation.

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Xuwen Chen, Shunlin Shen, Zhifei Zhang. 2025-01-24. $l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation. https://doi.org/10.1007/s00220-026-05614-4

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