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

学术报告

偏微分方程讨论班

Speaker: 张鑫（同济大学）

Inviter: 张平

Language: Chinese

Title：Local profiles of the self-similar solutions of the planar stationary Navier-Stokes equations

Time&Venue：2025年11月7日（星期五）15:00-16:00 & 南楼N913

Abstract: In this talk, we discuss self-similar solutions of the two-dimensional stationary incompressible Navier-Stokes (SNS) problem under scaling symmetries, which are also known as Jeffery-Hamel solutions. More recently, following some idea of G.Hamel (1917), V.Sverak (2011) proved the existence of smooth Jeffery-Hamel solutions under some zero flux condition. Using some new reduction process of (SNS) problem, we mainly prove that all the smooth Jeffery-Hamel solutions admit exactly two explicit forms without requiring any flux condition whenever the velocity fields only have the radial components. The key to our approach lies in the explicit classification of the local profiles of these solutions. This talk is based on a joint work with Ming Li (Tongji University), Linyu Peng (Keio University) and Ping Zhang (AMSS).