Local Rigidity of the Couette Flow for the Stationary Triple-Deck Equations
Analysis of PDEs
2024-05-20 v1
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.
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Cite
@article{arxiv.2405.10532,
title = {Local Rigidity of the Couette Flow for the Stationary Triple-Deck Equations},
author = {Sameer Iyer and Yasunori Maekawa},
journal= {arXiv preprint arXiv:2405.10532},
year = {2024}
}
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24 pages