Low-regularity global well-posedness for the Boltzmann equation near vacuum

We study the Boltzmann equation near vacuum in anisotropic low-regularity Besov spaces. We establish the global existence and uniqueness of strong solutions with the critical regularity index $2\mathrm{/}p$ for $p\in [1,\mathrm{\infty })$ in ${\mathbb{R}}^3$. The proof relies on a new bilinear estimate for the nonlinear collision operator. Combined with a div-curl type lemma we develop, this allows us to close the a priori estimates and thereby obtain global well-posedness.