# Stable Poiseuille flow transfer for a Navier-Stokes system

Abstract : We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also known as the Poisseuille flow, this problem is frequently cited as a paradigm for transition to turbulence. Our approach consists in generating an exact trajectory of the nonlinear system that approaches exponentially the objective profile. A boundary control law guarantees then that the error between the state and the trajectory decays exponentially in the $L^2$ norm. The result is first proved for the linearized Stokes equations, then shown to hold for the nonlinear Navier-Stokes system.
Document type :
Conference papers

Cited literature [17 references]

https://hal.archives-ouvertes.fr/hal-00086477
Contributor : Emmanuel Trélat <>
Submitted on : Tuesday, July 18, 2006 - 6:13:40 PM
Last modification on : Monday, December 23, 2019 - 3:50:10 PM
Long-term archiving on: Tuesday, September 18, 2012 - 4:20:32 PM

### Identifiers

• HAL Id : hal-00086477, version 1

### Citation

Rafael Vazquez, Emmanuel Trélat, Jean-Michel Coron. Stable Poiseuille flow transfer for a Navier-Stokes system. 2006, 6 p. ⟨hal-00086477⟩

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