Pseudospectral bound and transition threshold for the 3D Kolmogorov flow

Original · EN

In this paper, we establish the pseudospectral bound 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 [LWZ], we prove the sharp enhanced dissipation rate for the linearized Navier-Stokes equations. As an application, we prove that if the initial velocity satisfies U₀-(kf⁻²(kfy),0,0)ₕ₂≤ cν⁷/⁴ (ν the viscosity coefficient) and kf∈ (0,1), then the solution does not transition away from the Kolmogorov flow.