报告题目：Unbounded solutions to the 2d incompressible Euler equation

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

报告时间：2026年9月3日（星期四）9:00—9:45

报告地点：数学科学学院114

校内联系人：廖娴 教授 联系方式：84708351-8510

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 L^2) 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 $L^2$ 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.