Some controllability results for linearized compressible navier−stokes system
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1002-1028.

In this article, we study the null controllability of linearized compressible Navier−Stokes system in one and two dimension. We first study the one-dimensional compressible Navier−Stokes system for non-barotropic fluid linearized around a constant steady state. We prove that the linearized system around (ρ ¯,0,θ ¯), with ρ ¯>0,θ ¯>0 is not null controllable by localized interior control or by boundary control. But the system is null controllable by interior controls acting everywhere in the velocity and temperature equation for regular initial condition. We also prove that the the one-dimensional compressible Navier−Stokes system for non-barotropic fluid linearized around a constant steady state (ρ ¯,v ¯,θ ¯), with ρ ¯>0,v ¯>0,θ ¯>0 is not null controllable by localized interior control or by boundary control for small time T. Next we consider two-dimensional compressible Navier−Stokes system for barotropic fluid linearized around a constant steady state (ρ ¯,0). We prove that this system is also not null controllable by localized interior control.

DOI : 10.1051/cocv/2014056
Classification : 35Q30, 93C20, 93B05
Mots clés : Linearized compressible Navier−Stokes System, Null controllability, localized interior control, boundary control, Gaussian Beam
Maity, Debayan 1

1 Centre for Applicable Mathematics, TIFR, Post Bag No. 6503, GKVK Post Office, 560065 Bangalore, India.
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Maity, Debayan. Some controllability results for linearized compressible navier−stokes system. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1002-1028. doi : 10.1051/cocv/2014056. http://archive.numdam.org/articles/10.1051/cocv/2014056/

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