Pseudospectral Bound and Transition Threshold for the 3D Kolmogorov Flow. Issue 3 (23rd August 2019)

• Record Type: Journal Article
• Authors: Li, Te; Wei, Dongyi; Zhang, Zhifei
• Is Part Of: Communications on pure and applied mathematics. Volume 73:Issue 3(2020:Mar.)
• Page Start: 465
• Page End: 557
• Publication Date: 2019-08-23
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21863
• Languages: English
• ISSNs: 0010-3640

Abstract

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.