Advances in Differential Equations

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

Debanjana Mitra, Mythily Ramaswamy, and Jean-Pierre Raymond

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1495850457

Zentralblatt MATH identifier
1371.93099

Subjects
Primary: 93C20: Systems governed by partial differential equations 93D15: Stabilization of systems by feedback 76N25: Flow control and optimization

Citation

Mitra, Debanjana; Ramaswamy, Mythily; Raymond, Jean-Pierre. Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity. Adv. Differential Equations 22 (2017), no. 9/10, 693--736. https://projecteuclid.org/euclid.ade/1495850457


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