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: Haocheng Yang（ New York University Abu Dhabi）
Inviter: 张平
Language: Chinese
Title: Local Invariant Structures in the Dynamics of Capillary Water Jet
Time & Venue: 2026年5月11日（星期一）16：00-17：00 & 南楼N913
Abstract: The instability of the water jet system under long-wave perturbation—the Rayleigh-Plateau instability—has been observed and studied in experimental and theoretical physics since the 19th century. This talk provides a rigorous mathematical justification for this phenomenon. We consider the water jet system, modeled by the incompressible irrotational Euler equation with surface tension, and prove that it possesses a local hyperbolic structure around the trivial steady state. The core of our method is the construction of “paradifferential propagator" corresponding to linear paradifferential hyperbolic systems, effectively balancing the loss of regularity due to the quasilinear nature of this system. This enables the use of Lyapunov-Perron type arguments to construct the stable/unstable manifolds and a center invariant set, with or without spectral gap. We expect that such method could be extended to other quasilinear models. This is a joint work with Chengyang Shao.
附件：