Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff

Abstract

In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^{\infty }$ regularity in the velocity variable for the positive time.

References in corpus (2)

• Regularizing effect and local existence for non-cutoff Boltzmann equation
• The Boltzmann equation without angular cutoff in the whole space: III, Qualitative properties of solutions

Cited by in corpus (3)

• Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
• Measure valued solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• About the Landau-Fermi-Dirac equation with moderately soft potentials