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Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity. (English) Zbl 1371.93099

Summary: In this paper, we study the local stabilization of one dimensional compressible Navier-Stokes equations around a constant steady solution \((\rho_s, u_s)\), where \(\rho_s>0, u_s\neq 0\). In the case of periodic boundary conditions, we determine a distributed control acting only in the velocity equation, able to stabilize the system, locally around \((\rho_s, u_s)\), with an arbitrary exponential decay rate. In the case of Dirichlet boundary conditions, we determine boundary controls for the velocity and for the density at the inflow boundary, able to stabilize the system, locally around \((\rho_s, u_s)\), with an arbitrary exponential decay rate.

MSC:

93C20 Control/observation systems governed by partial differential equations
93D15 Stabilization of systems by feedback
76N25 Flow control and optimization for compressible fluids and gas dynamics
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Full Text: Euclid