Stability threshold of the two-dimensional Couette flow in the whole plane

Hui Li; Ning Liu; Weiren Zhao

doi:10.1016/j.jfa.2025.111271

Stability threshold of the two-dimensional Couette flow in the whole plane

Hui Li
, Ning Liu
, Weiren Zhao

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the stability threshold for the two-dimensional Couette flow in the whole plane. Our main result establishes that the asymptotic stability threshold is at most 13+ for Sobolev perturbations with additional control over low horizontal frequencies, aligning with the threshold results in periodic domains. As a secondary outcome of our approach, we also prove the asymptotic stability for perturbations in weak Sobolev regularity with size ν¹²[jls-end-space/].

Original language	English
Article number	111271
Journal	Journal of Functional Analysis
Volume	290
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2025.111271
Publication status	Published - 15 Feb 2026
Externally published	Yes

Keywords

Couette flow
Quasi-linearization
Sobolev spaces
Stability threshold
The whole plane

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10.1016/j.jfa.2025.111271

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title = "Stability threshold of the two-dimensional Couette flow in the whole plane",

abstract = "In this paper, we study the stability threshold for the two-dimensional Couette flow in the whole plane. Our main result establishes that the asymptotic stability threshold is at most 13+ for Sobolev perturbations with additional control over low horizontal frequencies, aligning with the threshold results in periodic domains. As a secondary outcome of our approach, we also prove the asymptotic stability for perturbations in weak Sobolev regularity with size ν12[jls-end-space/].",

keywords = "Couette flow, Quasi-linearization, Sobolev spaces, Stability threshold, The whole plane",

author = "Hui Li and Ning Liu and Weiren Zhao",

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AU - Liu, Ning

AU - Zhao, Weiren

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N2 - In this paper, we study the stability threshold for the two-dimensional Couette flow in the whole plane. Our main result establishes that the asymptotic stability threshold is at most 13+ for Sobolev perturbations with additional control over low horizontal frequencies, aligning with the threshold results in periodic domains. As a secondary outcome of our approach, we also prove the asymptotic stability for perturbations in weak Sobolev regularity with size ν12[jls-end-space/].

AB - In this paper, we study the stability threshold for the two-dimensional Couette flow in the whole plane. Our main result establishes that the asymptotic stability threshold is at most 13+ for Sobolev perturbations with additional control over low horizontal frequencies, aligning with the threshold results in periodic domains. As a secondary outcome of our approach, we also prove the asymptotic stability for perturbations in weak Sobolev regularity with size ν12[jls-end-space/].

KW - Couette flow

KW - Quasi-linearization

KW - Sobolev spaces

KW - Stability threshold

KW - The whole plane

UR - https://www.scopus.com/pages/publications/105023910433

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DO - 10.1016/j.jfa.2025.111271

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VL - 290

JO - Journal of Functional Analysis

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ER -

Stability threshold of the two-dimensional Couette flow in the whole plane

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Keywords

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