发表机构
University of Illinois at Chicago（芝加哥伊利诺伊大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维欧拉流线性化方程，利用Baldi坐标图识别临界环面，证明其Floquet指数为正，并通过几何光学构造将不稳定性提升，导致指数增长。
AI 中文摘要
我们研究了关于Gavrilov型光滑紧支撑平稳流线性化的三维（3D）不可压缩欧拉方程。Baldi的保体积作用-角坐标图允许在不变环面上约化高频振幅方程。利用Baldi坐标图，我们识别出一个由紧致截断确保的临界环面。我们证明，对于具有足够大法向分量的固定轴对称余向量，该环面上的约化无迹周期余循环是双曲的，并具有正Floquet指数。一个局部几何光学构造随后将此Floquet不稳定性提升到线性化欧拉方程，从而在空间$H^s$（$s\geq 0$）中产生指数本质范数增长。
英文摘要
We study the three-dimensional (3D) incompressible Euler equation linearized about a smooth compactly supported stationary flow of Gavrilov type. Baldi's volume-preserving action--angle chart allows a reduction of the high-frequency amplitude equation on invariant tori. Using Baldi's chart, we identify a critical torus ensured by the compact cutoff. We show that, for a fixed axisymmetric covector with sufficiently large normal component, the reduced trace-free periodic cocycle on this torus is hyperbolic and has a positive Floquet exponent. A localized geometric-optics construction then lifts this Floquet instability to the linearized Euler equation, yielding exponential essential-norm growth in space $H^s$, $s\geq 0$.
