JournalsaihpcVol. 33, No. 2pp. 529–574

Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations

  • Mehdi Badra

    Laboratoire LMAP, UMR CNRS 5142, Université de Pau et des Pays de l'Adour, F-64013 Pau Cedex, France
  • Sylvain Ervedoza

    Institut de Mathématiques de Toulouse; UMR5219; Université de Toulouse; CNRS; UPS IMT, F-31062 Toulouse Cedex 9, France
  • Sergio Guerrero

    Université Pierre et Marie Curie, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France
Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations cover
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Abstract

The goal of this article is to show a local exact controllability to smooth (C2C^{2}) trajectories for the density dependent incompressible Navier–Stokes equations. Our controllability result requires some geometric condition on the flow of the target trajectory, which is remanent from the transport equation satisfied by the density. The proof of this result uses a fixed point argument in suitable spaces adapted to a Carleman weight function that follows the flow of the target trajectory. Our result requires the proof of new Carleman estimates for heat and Stokes equations.

Cite this article

Mehdi Badra, Sylvain Ervedoza, Sergio Guerrero, Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 2, pp. 529–574

DOI 10.1016/J.ANIHPC.2014.11.006