The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential

TL;DR

This paper proves the global existence of solutions to the Boltzmann equation without angular cutoff for hard potentials in the whole space, assuming small perturbations around equilibrium, advancing mathematical understanding of kinetic theory.

Contribution

It establishes the global existence of solutions in weighted Sobolev spaces for the Boltzmann equation without angular cutoff, specifically for hard potentials, extending previous work.

Findings

Global existence of solutions proved for small perturbations

Solutions exist in weighted Sobolev spaces

Advances understanding of Boltzmann equation without angular cutoff

Abstract

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces for hard potential when the solution is a small perturbation of a global equilibrium.