Some solutions of the Boltzmann equation without angular cutoff

摘要

We show the existence of local or global in time solutions for the non-homogeneous Boltzmann equation. This is done under the assumptions that initial data are smaller than a suitable Maxwellian and that collisional cross-sections do not satisfy Grad's angular cutoff. Partial regularity in space-velocity of the solutions constructed herein is also proved. [References: 40]