Local well-posedness for Boltzmanns equation and the Boltzmann hierarchy via Wigner transform

We use the dispersive properties of the linear Schr{o}dinger equation to prove local well-posedness results for the Boltzmann equation and the related Boltzmann hierarchy, set in the spatial domain $mathbb{R}^d$ for $dgeq 2$. The proofs are based on the use of the (inverse) Wigner transform along with the spacetime Fourier transform. The norms for the initial data $f_0$ are weight