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

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

2012-02-04

arxiv.org/abs/1202.0910v1

Mathematics

Analysis of PDEs

Scientific paper

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 $T$.

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