## Advances in Differential Equations

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

#### Abstract

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.

#### Article information

Source
Adv. Differential Equations Volume 22, Number 9/10 (2017), 693-736.

Dates
First available in Project Euclid: 27 May 2017

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