Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4604101 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2016 | 46 Pages |
Abstract
The goal of this article is to show a local exact controllability to smooth (C2C2) 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mehdi Badra, Sylvain Ervedoza, Sergio Guerrero,