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The Dynamical Systems Approach to the Navier-Stokes Equations of Compressible Fluids

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Advances in Mathematical Fluid Mechanics

Abstract

We develop a dynamical system theory for the Navier-Stokes equations of isentropic compressible fluid flows in three space dimensions. Such a theory is based on a priori estimates, asymptotic compactness of solutions and an exact description of propagation of oscillations in the density component. The abstract theory yields several results concerning the long-time behaviour of solutions, in particular, the convergence towards a stationary state of a potential flow is proved.

. . . what we call objective reality is, in the last analysis, that which is common to several thinking beings, and could be common to all; this common part, we will see, can be nothing but the harmony expressed by mathematical laws. H. Poincare, La valeur de la science, p. 9.

The work was supported by Great 201/98/1450 GA ČR.

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Author information

Authors and Affiliations

  1. Institute of Mathematics AV ČR, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

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  1. Eduard Feireisl
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Editors and Affiliations

  1. Mathematical Institute, Charles University, Sokolovská 83, 18675, Prague 8, Czech Republic

    Josef Málek , Jindřich Nečas  & Mirko Rokyta ,  & 

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115-2888, USA

    Jindřich Nečas

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Feireisl, E. (2000). The Dynamical Systems Approach to the Navier-Stokes Equations of Compressible Fluids. In: Málek, J., Nečas, J., Rokyta, M. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57308-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-57308-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67786-4

  • Online ISBN: 978-3-642-57308-8

  • eBook Packages: Springer Book Archive

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