Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension

Debanjana Mitra; Mythily Ramaswamy; Jean-Pierre Raymond

doi:10.3934/mcrf.2015.5.259

Article Contents

2015, Volume 5, Issue 2: 259-290. Doi: 10.3934/mcrf.2015.5.259

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Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension

1.
T.I.F.R Centre for Applicable Mathematics, Post Bag No. 6503, GKVK Post Oce, Bangalore-560065
2.
Institut de Mathématiques de Toulouse, Université Paul Sabatier & CNRS, 31062 Toulouse Cedex

Received: May 2014

Revised: February 2015

Published: June 2015

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Abstract

In this paper we determine the largest space in which the linearized compressible Navier-Stokes system in one dimension, with periodic boundary conditions, is stabilizable with any prescribed exponential decay rate, by an interior control acting only in the velocity equation. As a consequence, it also follows that this largest space for the stabilizability with any prescribed exponential decay rate is also the largest one for the null controllability of the same system.

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Mathematics Subject Classification: Primary: 93C20, 93D15; Secondary: 34H05, 93B52, 35B35, 76N25.

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