发表机构
South China Normal University; The Chinese University of Hong Kong; University of Cambridge; Weizmann Institute of Science（华南师范大学; 香港中文大学; 剑桥大学; 魏茨曼科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文解决了二维粘性原始方程Leray-Hopf弱解唯一性的长期公开问题，证明了周期通道中满足特定边界条件、任意L²初始数据下该类弱解的唯一性。
AI 中文摘要
Lions、Temam和Wang在20世纪90年代证明了二维或三维粘性原始方程的Leray-Hopf型弱解的整体存在性，但此后无论是二维还是三维情形下的相应唯一性问题，都成为了一个长期悬而未决的公开问题。本文在二维情形下解决了该公开问题，具体而言，我们证明了在周期通道中、固体边界满足不可渗透和无应力边界条件、具有任意L²初始数据的粘性原始方程的Leray-Hopf弱解的唯一性。
英文摘要
Global existence of Leray-Hopf (type) weak solutions to the viscous primitive equations in two or three dimensions was established by Lions--Temam--Wang \cite{Lions1,Lions2,Lions3,Lions4} in the 1990s; however, the corresponding uniqueness, no matter in two or three dimensions, has been a long standing open problem since then. In this paper, we solve this open problem in the two-dimensional case. Precisely, we prove the uniqueness of Leray-Hopf weak solutions, with arbitrary $L^2$ initial data, to the viscous primitive equations in a periodic channel, subject to impermeability and stress-free boundary conditions on the solid boundaries.
