11 

The Boltzmann equation with cutoff Rutherford scattering cross section

主讲人：周玉龙

摘要：The 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 and ill-posedness of the Boltzmann equation. Under some cutoff on the deviation angle, in 1936 L. D. Landau derived a new equation for the weakly interacting gas which is now referred to as the Fokker-Planck-Landau or Landau equation. In this talk, we will show how to justify Landau's formal derivation and simultaneously solve the so-called Landau approximation problem proposed by Alexandre and Villani in 2004. More precisely, in this talk we will discuss (i) global well-posedness of the Boltzmann equation with cutoff Rutherford cross section. (ii). a logarithmic global-in-time error estimate between solutions to the Boltzmann and Landau equations, which is consistent with the famous Coulomb logarithm. This is based on a joint work with Prof. Ling-Bing He.

主讲人简介：周玉龙，中山大学副教授，硕士生导师。主要从事动理学方程的理论研究，包括Boltzmann方程和Landau方程，研究成果发表在Arch. Ration. Mech. Anal.、Ann. Inst. H. Poincaré Anal. Non Linéaire、SIAM J. Control Optim. 等期刊上。

邀请人：雷远杰

时间：2022年5月24日（星期二）14:00-16:00

地点：腾讯会议室     ID:413289111