报告题目：The Fermi–Pasta–Ulam system and the Korteweg–de–Vries equation: A low-regularity continuum limit

报 告 人：Herbert Koch (Professor @ UB - University of Bonn)

报告时间：2026年9月1日（星期二）10:00—11:30

报告地点：数学科学学院115（大报告厅）

校内联系人：赵磊 教授    联系方式：84708351-8625

Abstract: For the infinite Fermi–Pasta–Ulam (FPU) system, general solutions can be approximated 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 $L^2$-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.