Volume 24, Number 1, January–March 2018
|Page(s)||211 - 235|
|Published online||17 January 2018|
Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations
Institut de Mathématiques de Toulouse, UMR5219; Université de Toulouse, CNRS, UPS IMT, 31062 Toulouse Cedex 9, France.
Corresponding author: email@example.com
Received: 21 September 2015
Revised: 26 September 2016
In this article, we show a local exact boundary controllability result for the 1d isentropic compressible Navier Stokes equations around a smooth target trajectory. Our controllability result requires a geometric condition on the flow of the target trajectory, which comes naturally when dealing with the linearized equations. The proof of our result is based on a fixed point argument in weighted spaces and follows the strategy already developed in [S. Ervedoza, O. Glass, S. Guerrero, J.-P. Puel, Arch. Ration. Mech. Anal. 206 (2012) 189–238] in the case of a non-zero constant velocity field. The main novelty of this article is in the construction of the controlled density in the case of possible oscillations of the characteristics of the target flow on the boundary.
Mathematics Subject Classification: 35Q30 / 93B05 / 93C20
Key words: Local Controllability / compressible Navier-Stokes equations
© EDP Sciences, SMAI 2018
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