Global classical solutions of the Boltzmann equation without angular cut-off

@article{Gressman2009GlobalCS,
title={Global classical solutions of the Boltzmann equation without angular cut-off},
author={P. Gressman and Robert M. Strain},
journal={Journal of the American Mathematical Society},
year={2009},
volume={24},
pages={771-847}
}
• Published 2009
• Physics, Mathematics
• Journal of the American Mathematical Society
This work proves the global stability of the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse-power intermolecular potentials, $r^{-(p-1)}$ with $p>2$, for initial perturbations of the Maxwellian equilibrium states, as announced in \cite{gsNonCutA}. We more generally cover collision kernels with parameters $s\in (0,1)$ and $\gamma$ satisfying $\gamma > -n$ in arbitrary dimensions $\mathbb{T}^n \times \mathbb{R}^n$ with $n\ge… Expand 160 Citations Optimal time decay of the non cut-off Boltzmann equation in the whole space In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole spaceExpand Moments and Regularity for a Boltzmann Equation via Wigner Transform • Mathematics, Physics • 2018 In this paper, we continue our study of the Boltzmann equation by use of tools originating from the analysis of dispersive equations in quantum dynamics. Specifically, we focus on properties ofExpand Stability of Vacuum for the Landau Equation with Moderately Soft Potentials • J. 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