Transition threshold for the Navier–Stokes–Coriolis system at high Reynolds numbers

Abstract In this paper, we study the transition threshold for Couette flow in the three‐dimensional incompressible Navier–Stokes–Coriolis system in the high‐Reynolds‐number regime (). By combining the stabilizing effects of rotation‐induced dispersion and mixing, we obtain an improved stability threshold in . More precisely, we prove global stability for perturbations of size in when the fluid domain and , and in when and . The corresponding solution exists globally and remains asymptotically close to the Couette flow. The main difficulty lies in the anisotropic nature of the estimates for the zero modes and in their interaction with the nonzero modes. To overcome this difficulty, we introduce anisotropic Sobolev spaces tailored to the zero modes, identify a new dispersive structure for these modes, and establish suitable Strichartz‐type estimates. These ingredients allow us to exploit both the nonlinear structure and the improved dispersion of certain favorable zero‐mode components.