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科学研究
RESEARCH
On the Fokker-Planck-Landau equation: derivation, weak coupling limit and well-posedness
时间  Datetime
2019-07-29 10:30 — 11:30
地点  Venue
Zoom APP()
报告人  Speaker
He Lingbing
单位  Affiliation
清华大学
邀请人  Host
杨雄锋
备注  remarks
会议号码: 639 934 97672 会议密码:656106
报告摘要  Abstract

凯时kb88.comThe well-known Rutherford differential  cross section corresponds to a two body interaction with  Coulomb potential.   It leads to the logarithmically divergence of the momentum transfer (or the transport cross section). In reality  we  assume that  $ heta_{min}$ is the order of magnitude of the smallest angles for which the scattering can still be regarded as Coulomb scattering. Under ad hoc cutoff on the deviation angle, L. D. Landau derived a new equation for the weakly interacting gas which is now named after him. In this talk, we will present our results as follows:

凯时kb88.com(i). we prove global well-posedness of the Boltzmann equation with cutoff Rutherford scattering cross section near Maxwellian. As a result, we rigorously justify Landau's formal derivation  globally in time;

(ii). we revisit Landau approximation problem and prove a global-in-time error estimate between solutions to Boltzmann and Landau equations with logarithm accuracy, which is consistent with the famous Coulomb logarithm.  Key ingredients into the proofs of these results include a complete description of the linearized Boltzmann collision operator, a uniform spectral gap estimate and a novel linear-quasilinear method.