走向现代数学学术报告 - 王国栋副教授（No. 815)

报告题目: Orbital stability of first Laplacian eigenstates for the Euler equation on flat 2-tori

报告时间：2025年10月24日 8:30

报告地点：东海岸校区-D实209

报 告 人：王国栋 副教授（大连理工大学）

邀 请 人：王大斌 教授

报告摘要：On a flat 2-torus, the Laplacian eigenfunctions can be expressed in terms of sinusoidal functions. For a rectangular or square torus, it is known that every first eigenstate is orbitally stable up to translation under the Euler dynamics. In this talk, we show that this is also true for flat tori of arbitrary shape. As a corollary, we obtain for the first time a family of orbitally stable sinusoidal Euler flows on a hexagonal torus. The proof is carried out within the framework of Burton's stability criterion and consists of two key ingredients: (i) establishing a suitable variational characterization for each equimeasurable class in the first eigenspace, and (ii) analyzing the number of translational orbits within each equimeasurable class.

报告人简介：王国栋，大连理工大学数学科学学院副教授，博士生导师。2019年博士毕业于中科院数学与系统科学研究院，曾在哈尔滨工业大学数学研究院任师资博士后。研究方向为非线性偏微分方程，具体包括：不可压缩Euler方程定常解的构造、点涡的去奇异化、解的Lyapunov稳定性等。在Math. Ann., Trans. AMS, JFA, SIAM J. Math. Anal., CVPDE等学术期刊发表学术论文20余篇，现主持国家自然基金委面上项目一项，曾主持完成国家自然基金委青年基金一项、博士后面上和特别资助各一项。