Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation

In the paper, for Cauchy problem on non-cutoff Boltzmann equation in torus, we establish global-in-time Gevrey smoothness velocity and space variables a class of low-regularity mild solutions near Maxwellians with index depending only angular singularity. This together [24] provides self-contained well-posedness theory both existence regularity global initial data low framework perturbations. For proof treat subtle way commutator between regularization operators collision operator involving rough coefficients, this enables us to combine classical Hörmander's hypoelliptic techniques symbolic calculus established linearized so as improve at positive time.