Optimal control of linearized compressible Navier–Stokes equations

Shirshendu Chowdhury; Mythily Ramaswamy

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 2, page 587-615
  • ISSN: 1292-8119

Abstract

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We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over the control set. Finally we derive an optimality system from which the optimal solution can be determined.

How to cite

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Chowdhury, Shirshendu, and Ramaswamy, Mythily. "Optimal control of linearized compressible Navier–Stokes equations." ESAIM: Control, Optimisation and Calculus of Variations 19.2 (2013): 587-615. <http://eudml.org/doc/272922>.

@article{Chowdhury2013,
abstract = {We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over the control set. Finally we derive an optimality system from which the optimal solution can be determined.},
author = {Chowdhury, Shirshendu, Ramaswamy, Mythily},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal control; linearized compressible Navier–Stokes equations; boundary control; optimality system; linearized compressible Navier-Stokes equations},
language = {eng},
number = {2},
pages = {587-615},
publisher = {EDP-Sciences},
title = {Optimal control of linearized compressible Navier–Stokes equations},
url = {http://eudml.org/doc/272922},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Chowdhury, Shirshendu
AU - Ramaswamy, Mythily
TI - Optimal control of linearized compressible Navier–Stokes equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 2
SP - 587
EP - 615
AB - We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over the control set. Finally we derive an optimality system from which the optimal solution can be determined.
LA - eng
KW - optimal control; linearized compressible Navier–Stokes equations; boundary control; optimality system; linearized compressible Navier-Stokes equations
UR - http://eudml.org/doc/272922
ER -

References

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  9. [9] J.P. Raymond, Stokes and Navier–Stokes equations with nonhomogeneous boundary conditions. Ann. Inst. Henri Poincaré Anal. Non Linéaire24 (2007) 921–951. Zbl1136.35070MR2371113
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