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# 数学学科现代分析及其应用研究所（2020非线性分析与偏微分方程系列报告会三十三）

 报告题目65：Boltzmann equation with cutoff Rutherford cross section near Maxwellian报 告 人：何凌冰（清华大学）会议时间：12月16日（周三），18：30-19：30腾讯会议ID:  478 869 168，https://meeting.tencent.com/s/mOwlLFtbO7VL 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 (or the transport cross section). In reality  we  assume that  $\theta_{min}$ 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:(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.报告人简介：何凌冰教授，清华大学数学系，博士毕业于中科院，主要研究方向为微局部分析与偏微分方程，研究领域集中在动理学方程和流体力学方程的适定性，解的长时间行为以及相应的渐进分析等问题上。学术成果主要发表于Arch. Ration. Mech. Anal.,J. Funct.Anal，Comm. Math. Phys等国际数学期刊上。邀请人：非线性分析与PDE团队