Global Existence of Non-cutoff Boltzmann Equation in Weighted Sobolev Space

Abstract

This article presents a new approach of semigroup analysis and pseudo-differential calculus for deriving the regularizing estimate on non-cutoff linearized Boltzmann equation. We are able to obtain regularizing estimate of semigroup $e^{tB}$ that is continuous from weighted Sobolev space $H(a^{-1/2})H_x^m$ to $H(a^{1/2})H_x^m$ with a sharp large time decay. With these properties, we prove the existence of global-in-time unique solution to the non-cutoff Boltzmann equation for hard potential on the whole space with weak regularity assumption on initial data. We consider the hard potential case since $H(a^{1/2})$ can be embedded in $L^2$. This work develops the application of pseudo-differential calculus, spectrum analysis and semigroup theory to non-cutoff Boltzmann equation.

References in corpus (4)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff
• Regularity of Non-cutoff Boltzmann Equation with Hard Potential
• Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation

Cited by in corpus (1)

• Non-cutoff Boltzmann equation with soft potentials in the whole space