The Landau equation does not blow up
数学专题报告
报告题目(Title)：The Landau equation does not blow up
报告人(Speaker)：Luis Silvestre (University of Chicago)
地点(Place)：ZoomID: 967 1736 3318, PWD: 679489
时间(Time)：2024 年 2月 23日 9：30—10：30
邀请人(Inviter)：熊金钢
报告摘要
The Landau equation is one of the main equations in kinetic theory. It models the evolution of the density of particles when they are assumed to repel each other by Coulomb potentials. It is a limit case of the Boltzmann equation with very soft potentials. In the space-homogeneous case, we show that the Fisher information is monotone decreasing in time. As a consequence, we deduce that for any initial data the solutions stay smooth and never blow up, closing a well-known open problem in the area.
* This PDE seminar is co-organized with Tianling Jin at The Hong Kong University of Science and Technology. See the seminar webpage:
https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
