Pseudospectral Bound and Transition Threshold for the 3D Kolmogorov Flow

Source 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 urn:x-wiley:00103640:media:cpa21863:cpa21863-math-0001 ( ν the viscosity coefficient) and k f ∈ (0, 1), then the solution does not transition away from the Kolmogorov flow. © 2019 Wiley Periodicals, Inc.