Compressible Navier-Stokes equations

Pavel I. Plotnikov; Jan Sokolowski

doi:10.3934/proc.2009.2009.602

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2009, Volume 2009: 602-611. Doi: 10.3934/proc.2009.2009.602 open access

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Compressible Navier-Stokes equations

Pavel I. Plotnikov^1, and
Jan Sokolowski^2,

1.
Lavryentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences, Lavryentyev pr. 15, Novosibirsk 630090
2.
Institut Elie Cartan, UMR 7502 (Nancy Université, CNRS, INRIA), Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-lès-Nancy, Cedex

Received: August 2008

Revised: April 2009

Published: August 2009

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Abstract

Compressible, stationary Navier-Stokes (N-S) equations are considered. The shape sensitivity analysis is performed in the case of small perturbations of the so-called it approximate solutions. The proposed method of shape sensitivity analysis is general, and can be used to establish the well-posedness for distributed and boundary control problems as well as for inverse problems in the case of the state equations in the form of compressible N-S equations.

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Mathematics Subject Classification: Primary: 76N10; 35Q30; Secondary: 35A15; 76N15.

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