Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity
2017
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.
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