Global Mild Solutions of the Landau and Non‐Cutoff Boltzmann Equations

• Published in: Communications on pure and applied mathematics Vol. 74; no. 5; pp. 932 - 1020
• Main Authors: Duan, Renjun, Liu, Shuangqian, Sakamoto, Shota, Strain, Robert M.
• Format: Journal Article
• Language: English
• Published: Melbourne John Wiley & Sons Australia, Ltd 01.05.2021; John Wiley and Sons, Limited
• Subjects: Boltzmann transport equation; Boundary conditions; Boundary value problems; Coulomb potential; Distribution functions; Domains; Function space; Mathematical analysis; Operators (mathematics); Regularity; Sobolev space; Specular reflection; Toruses; Variables

This paper proves the existence of small‐amplitude global‐in‐time unique mild solutions to both the Landau equation including the Coulomb potential and the Boltzmann equation without angular cutoff. Since the well‐known works [45] and [3, 43] on the construction of classical solutions in smooth Sobo...