发表机构
Institute for Advanced Study, Shenzhen University; Department of Mathematics, Kunming University of Science and Technology（深圳大学高等研究院; 昆明理工大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明从非均匀剪切流分岔出的对称双周期三维小振幅流体弹性波在首阶上必为二维，降维由剪切流垂直结构控制且对边界条件变化稳健。
AI 中文摘要
本文证明，从非均匀剪切流分岔出的对称、双周期、三维小振幅流体弹性波，在首阶上必然是二维的。对二次阶可解性条件的详细分析表明，所有具有横向依赖性的傅里叶系数均恒为零。这种降维完全由剪切流的垂直结构控制，并且对动态边界条件的变化具有稳健性。
英文摘要
In this paper, we prove that symmetric, doubly-periodic, three-dimensional hydroelastic waves of small amplitude, bifurcating from a non-uniform shear flow, are necessarily two-dimensional to leading order. A detailed analysis of the solvability condition at quadratic order reveals that all Fourier coefficients with transverse dependence vanish identically. The dimensional reduction is controlled entirely by the vertical structure of the shear flow and is robust under changes to the dynamic boundary condition.
