Local rigidity of the Couette flow for the stationary triple-deck equations
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 tripledeck 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.
Fields of Study & Subjects
Fluid Dynamics and Turbulent Flows
Navier-Stokes equation solutions
Differential Equations and Numerical Methods
Publication details
- Journal / source
- Analysis & PDE
- Volume
- 19
- Issue
- 6
- Pages
- 1165–1189
- Publication date
- 13 July 2026
- Language
- EN