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
偏微分方程讨论班
Speaker: Pro.Herbert Koch （德国波恩大学）
Inviter:张翼
Language: English
Title: Unbounded solutions to the 2d incompressible Euler equation
Time & Venue：2026年9月14日（星期一） 10:00-11:00 南楼202
Abstract: In this talk, we study unbounded solutions of the 2D incompressible Euler equations. One of the motivating factors for this is that the usual functional framework for the Euler equations (e.g. based on finite energy conditions, such as L²) does not respect some of the symmetries of the problem, such as Galileo invariance. The first result, global existence and uniqueness of solutions for initial data with square-root growth O(|x|^{1/2−}) and bounded vorticity, is based on two key ingredients. Firstly an integral decomposition of the pressure, and secondly examining local energy balance leading to solution estimates in weighted L² spaces. We also prove continuity of the initial data to solution map by a substantial adaptation of Yudovich's uniqueness argument. The second result is global existence and uniqueness of solutions for initial data with sublinear growth O(|x|^{1−}). Here the Galileo symmetry plays an essential role, since the Leray projection is not available anymore. This is joint work with Dimitri Cobb. The first part recently appeared online in ARMA, the second part is work in progress.
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