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In this paper, we prove the linear stability of the pipe Poiseuille flow forgeneral perturbations at high Reynolds number regime. This is a long-standingproblem since the experiments of Reynolds in 1883. Our work lays a foundationfor the theoretical analysis of hydrodynamic stability of pipe flow, which isone of the oldest yet unsolved problems of fundamental fluid dynamics.

Linear stability of pipe Poiseuille flow at high Reynolds number regime