中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: Professor Norbert J. Mauser (WPI c/o U. Wien & Inst. CNRS Pauli)
Inviter: 张平
Language: English
Title: "(Asymptotic) Analysis of PDEs in Relativistic Quantum Physics: from Dirac-Maxwell to Euler-Poisson"
Time & Venue: 2026年4月1日（星期三）16：00-17：00 & N913
Abstract:We present the relativistic quantum physics model hierarchy from Dirac-Maxwell to Vlasov/Euler-Poisson that models fast moving charges
and their self-consistent electro-magnetic field.Our main interest is (asymptotic) analysis of these nonlinear time-dependent PDE, with focus on the Pauli-Poisswell/Darwin system which is the consistent model at first/second order in 1/c (c = speed of
light) that keeps both relativistic effects "spin" and "magnetism" and it's classical limit to selfconsistent kinetic/fluid equations, i.e. Vlasov/Euler - Poiswell/Darwin.Emphasis is on the (semi)classicial limit for vanishing Planck constant. We use both WKB methods and Wigner functions where we extend the 1993
results of P.L.Lions & Paul and Markowich & Mauser on the limit from Schrödinger-Poisson to Vlasov-Poisson, with similar subtilities of pure quantum states vs mixed states.In the hope of taming the mathematical complications stemming from the magnetic field, we are interested also in developping "quantum/semiclassical velocity averaging lemmata" building on the 1988 ideas of Golse, Perthame, Sentis and P.L.Lions.This talk aims to explain the models, the new results & ideas of proofs/techniques, as worked out in joint works mainly with Jakob Möller (X & WPI) and also Pierre Germain (U.Wien), Changhe Yang (Caltech), Francois Golse (X).
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