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September/October 2017 Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity
Debanjana Mitra, Mythily Ramaswamy, Jean-Pierre Raymond
Adv. Differential Equations 22(9/10): 693-736 (September/October 2017).

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.

Citation

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Debanjana Mitra. Mythily Ramaswamy. Jean-Pierre Raymond. "Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity." Adv. Differential Equations 22 (9/10) 693 - 736, September/October 2017.

Information

Published: September/October 2017
First available in Project Euclid: 27 May 2017

zbMATH: 1371.93099
MathSciNet: MR3656490

Subjects:
Primary: 76N25, 93C20, 93D15

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.22 • No. 9/10 • September/October 2017
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