The Boltzmann equation without angular cutoff in the whole space: III, Qualitative properties of solutions

Abstract

This is a continuation of our series of works for the inhomogeneous Boltzmann equation. We study qualitative properties of classical solutions, precisely, the full regularization in all variables, uniqueness, non-negativity and convergence rate to the equilibrium. Together with the results of Parts I and II about the well posedness of the Cauchy problem around Maxwellian, we conclude this series with a satisfactory mathematical theory for Boltzmann equation without angular cutoff.

References in corpus (6)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Global Strong Solutions of the Boltzmann Equation without Angular Cut-off
• Global Classical Solutions of the Boltzmann Equation with Long-Range Interactions and Soft Potentials
• The Gevrey hypoellipticity for kinetic equations
• Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential
• Gevrey hypoellipticity for a class of kinetic equations

Cited by in corpus (24)

• The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space
• Optimal Large-Time Behavior of the Vlasov-Maxwell-Boltzmann System in the Whole Space
• Optimal time decay of the non cut-off Boltzmann equation in the whole space
• Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff
• Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off
• Measure valued solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff
• Analytical regularizing effect for the radial and spatially homogeneous Boltzmann equation
• The Enskog process for hard and soft potentials
• Global Classical Solutions to the Relativistic Boltzmann Equation without Angular Cut-off
• Non-Cutoff Boltzmann Equation with Polynomial Decay Perturbation
• Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off
• Regularity of Non-cutoff Boltzmann Equation with Hard Potential
• The Vlasov-Poisson-Boltzmann System for Soft Potentials
• Non-cutoff Boltzmann equation with soft potentials in the whole space
• Global Existence of Non-cutoff Boltzmann Equation in Weighted Sobolev Space
• Global Well-posedness of the Relativistic Boltzmann Equation
• Sharp bounds for Boltzmann and Landau collision operators
• Global solution and time decay of the Vlasov-Poisson-Landau system in R3
• Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff
• Global well-posedness in spatially critical Besov space for the Boltzmann equation
• Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation
• The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space
• Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules