English

Remarks on global controllability for the shallow-water system with two control forces

Analysis of PDEs 2012-02-07 v1

Abstract

In this paper we deal with the compressible Navier-Stokes equations with a friction term in one dimension on an interval. We study the exact controllability properties of this equation with general initial condition when the boundary control is acting at both endpoints of the interval. Inspired by the work of Guerrero and Imanuvilov in \cite{GI} on the viscous Burger equation, we prove by choosing irrotational data and using the notion of effective velocity developed in \cite{cpde,cras} that the exact global controllability result does not hold for any time TT.

Keywords

Cite

@article{arxiv.1202.0910,
  title  = {Remarks on global controllability for the shallow-water system with two control forces},
  author = {Abdelmalek Drici and Boris Haspot},
  journal= {arXiv preprint arXiv:1202.0910},
  year   = {2012}
}
R2 v1 2026-06-21T20:14:53.030Z