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arXiv · 2509.06089

Unstable mode around the 3D boundary layer flow

Cheng-Jie Liu·Mengjun Ma·Di Wu·Zhu Zhang
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Abstract

We study the stability properties of boundary layer-type shear flows for the three-dimensional Navier-Stokes equations in the limit of small viscosity $0<\nu\ll 1$. When the streamwise and spanwise velocity profiles are linearly independent near the boundary, we construct an unstable mode that exhibits rapid growth at the rate of $e^{t/\sqrt{\nu}}$. Our results reveal an analytic instability in the three-dimensional Navier-Stokes equations around generic boundary layer profiles. This instability arises from the interplay between spanwise flow and three-dimensional perturbations, and does not occur in purely two-dimensional flows.

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Cheng-Jie Liu, Mengjun Ma, Di Wu, Zhu Zhang. 2025-09-07. Unstable mode around the 3D boundary layer flow. https://arxiv.org/abs/2509.06089

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