报告题目：Local Invariant Structures in the Dynamics of Capillary Water Jet

报 告 人：杨昊澄 (PostDoc @ NYUAD - New York University Abu Dhabi)

报告时间：2026年4月2日（星期四）9:00—9:45

报告地点：数学科学学院114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

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.