Chowdhury, S.; Ramaswamy, M.; Raymond, J.-P. Controllability and stabilizability of the linearized compressible Navier-Stokes system in one dimension. (English) Zbl 1257.93016 SIAM J. Control Optim. 50, No. 5, 2959-2987 (2012). Summary: In this paper, we consider the one-dimensional compressible Navier–Stokes system linearized about a constant steady state \((Q_0, 0)\) with \(Q_0 > 0\). We study the controllability and stabilizability of this linearized system. We establish that the linearized system is null controllable for regular initial data by an interior control acting everywhere in the velocity equation. We prove that this result is sharp by showing that the null controllability cannot be achieved by a localized interior control or by a boundary control acting only in the velocity equation. On the other hand, we show that the system is approximately controllable. We also show that the system is not stabilizable with a decay rate \(e^{-\omega t}\) for \(\omega > {\omega}_0\), where \({\omega}_0\) is an accumulation point of the real eigenvalues of the linearized operator. Cited in 1 ReviewCited in 30 Documents MSC: 93B05 Controllability 93D15 Stabilization of systems by feedback 35Q30 Navier-Stokes equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 93B18 Linearizations 93C20 Control/observation systems governed by partial differential equations Keywords:linearized compressible Navier-Stokes system; null controllability; boundary control; localized interior control; approximate controllability; stabilizality PDFBibTeX XMLCite \textit{S. Chowdhury} et al., SIAM J. Control Optim. 50, No. 5, 2959--2987 (2012; Zbl 1257.93016) Full Text: DOI Link