Pseudospectral Bound and Transition Threshold for the 3D Kolmogorov Flow

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 equati...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2020-03, Vol.73 (3), p.465-557
Main Authors: Li, Te, Wei, Dongyi, Zhang, Zhifei
Format: Article
Language:English
Subjects:
Fluid dynamics
Fluid flow
Linearization
Mathematical analysis
Three dimensional flow
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Summary: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∥U0−kf−2sinkfy,0,0∥H2≤cν7/4 (ν the viscosity coefficient) and kf ∈ (0, 1), then the solution does not transition away from the Kolmogorov flow. © 2019 Wiley Periodicals, Inc.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21863