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Pseudospectral Bound and Transition Threshold for the 3D Kolmogorov Flow
Author(s) -
Li Te,
Wei Dongyi,
Zhang Zhifei
Publication year - 2020
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21863
Subject(s) - mathematics , navier–stokes equations , operator (biology) , flow (mathematics) , dissipation , mathematical analysis , upper and lower bounds , mechanics , physics , geometry , thermodynamics , compressibility , biochemistry , chemistry , repressor , transcription factor , gene
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 sink 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.