报告人：徐欢（澳门大学）

时  间：2026年9月28日15:00

地  点：海韵园行政楼C610

内容摘要:

We study two-dimensional steady incompressible Euler flows with finite total curvature. A distinguished family of such flows arises from finite-Morse-index solutions to semilinear elliptic equations in two dimensions. We establish three main properties of finite-total-curvature flows in the \(L^\infty \cap H^1_{\text{loc}}\) class. First, in the plane and the half-plane, every such flow without essential stagnation points is a parallel shear flow. Second, in the plane, the half-plane, and the infinite strip, the pressure converges uniformly to a constant at each end at infinity. Third, in the plane, the half-plane, the infinite strip, and the periodic strip, we establish sharp lower bounds for the total curvature in terms of the pressure oscillation.The rigidity result in fact extends to a broader class of flows: in the plane and the half-plane, any steady Euler flow without stagnation points is a parallel shear flow provided that \(\nabla P \in L^q\) for some \(1 \le q \le 2\). Combined with standard elliptic estimates for the pressure, this result yields a new proof of Hamel and Nadirashvili's rigidity theorems, with the regularity assumption sharpened optimally to \(H^1_{\text{loc}}\).The pressure serves as a unifying quantity throughout the analysis.

个人简介：

徐欢，2021年获得美国奥本大学博士学位，随后在美国德州大学圣安东尼奥分校从事博士后研究，目前正在澳门大学进行博士后工作。其主要研究兴趣包括：二维Euler方程稳态解的分类、Navier-Stokes方程及相关发展方程解的全局正则性。徐博士在Comm. Math. Phys., Arch. Ration. Mech. Anal., J. Differential Equations, J. Evol. Equ., J. Math. Fluid Mech., J. Geom. Anal. 等国际知名期刊上发表了多篇学术论文。

联系人：詹伟城