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

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 Schrödinger equation.

Revised per the referee report. To appear in Comm. Math. Phys