Pseudospectral Bound and Transition Threshold for the 3D Kolmogorov Flow. Issue 3 (23rd August 2019) - Li, Te; Wei, Dongyi; Zhang, Zhifei
Abstract : In this paper, we study pseudospectral bounds for the linearized operator of the Navier‐Stokes equations around the 3D Kolmogorov flow. Using the pseudospectral bound and the wave operator method introduced in [22], we prove the sharp enhanced dissipation rate for the linearized Navier‐Stokes equations. As an application, we prove that if the initial velocity satisfies ∥ U 0 − k f − 2 sin k f y, 0, 0 ∥ H 2 ≤ c ν 7 / 4 ( ν the viscosity coefficient) and k f ∈ (0, 1), then the solution does not transition away from the Kolmogorov flow. © 2019 Wiley Periodicals, Inc.