Local rigidity of the Couette flow for the stationary triple-deck equations

Iyer, Sameer; Maekawa, Yasunori

doi:10.2140/apde.2026.19.1165

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Local rigidity of the Couette flow for the stationary triple-deck equations

Sameer Iyer and Yasunori Maekawa

Vol. 19 (2026), No. 6, 1165–1189

DOI: 10.2140/apde.2026.19.1165

Abstract

The triple-deck equations are a classical boundary layer model which describes the asymptotics of a viscous flow near the separation point, and the Couette flow is an exact stationary solution to the triple-deck equations. In this paper we prove the local rigidity of the Couette flow in the sense that there are no other stationary solutions near the Couette flow in a scale invariant space. This provides a stark contrast to the well-studied stationary Prandtl counterpart, and in particular offers a first result towards the rigidity question raised by R. E. Meyer in 1983.

Keywords

triple-deck, boundary layer separation

Mathematical Subject Classification

Primary: 76D10

Milestones

Received: 16 May 2024

Revised: 27 April 2025

Accepted: 27 August 2025

Published: 13 July 2026

Authors

Sameer Iyer
Department of Mathematics University of California, Davis Davis, CA United States

Yasunori Maekawa
Department of Mathematics Kyoto University Kyoto Japan

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Vol. 19, No. 6, 2026