Analysis and PDE Seminar——The Fermi-Pasta-Ulam system and the Korteweg-de-Vries equation: A low-regularity continuum limit
报告人：Herbert Koch (University of Bonn)
时间：2026-09-07 16:00-17:00
地点：王选报告厅
Abstract: For the infinite Fermi-Pasta-Ulam (FPU) system, general solutions can be approx-imated by counter-propagating waves associated with solutions to the Korteweg-de Vries (KdV) equation as the lattice mesh size goes to zero. The Toda lattice is a special case of the FPU system. We show that, by exploiting the conservation of the FPU Hamiltonian, the continuum limit from the FPU system to the KdV equation with L2-level initial data holds in appropriate norms on an arbitrary time interval, thereby answering an open question posed by Hong, Kwak, and Yang (2021). Moreover, for the local-in-time continuum limit of the FPU system to the KdV equation, we lower the required Sobolev regularity to H^s with s > − 3/4 . To establish this low-regularity continuum limit, we prove key trilinear estimates that are sharp up to the endpoint by combining linear estimates, the transversality of characteristic curves, and multilinear dispersive smoothing properties of the linear FPU flow. This is joint work with Ruoyuan Liu.
