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On Compactness, Domain Dependence and Existence of Steady State Solutions to Compressible Isothermal Navier–Stokes Equations

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Abstract.

The steady state system of isothermal Navier–Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of minimisation of the drag with respect to the admissible shape of the obstacle is defined. The generalized solutions for the Navier–Stokes equations are introduced. The existence of an optimal shape is proved in the class of admissible domains. In general the solutions are not unique for the problem under considerations.

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Authors and Affiliations

  1. Lavryentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences, Lavryentyev pr. 15, Novosibirsk, 630090, Russia

    P. I. Plotnikov

  2. Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré, Nancy I, B.P. 239, 54506, Vandoeuvre lès Nancy Cedex, France

    J. Sokolowski

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  1. P. I. Plotnikov
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  2. J. Sokolowski
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Correspondence to P. I. Plotnikov.

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Plotnikov, P.I., Sokolowski, J. On Compactness, Domain Dependence and Existence of Steady State Solutions to Compressible Isothermal Navier–Stokes Equations. J. math. fluid mech. 7, 529–573 (2005). https://doi.org/10.1007/s00021-004-0134-6

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  • DOI: https://doi.org/10.1007/s00021-004-0134-6

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