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Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations

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Abstract

The existence of a (global in time) solution to the Navier-Stokes equations for barotropic compressible fluids in a bounded interval is already known in the case of vanishing external force field. In this paper we consider these equations for time-independent forces and prove that: (i) there exists a global solution to the usual initial-boundary value problem; (ii) the density of the fluid is bounded and its infimum is greater than zero for infinite time only if the external forces and the pressure satisfy a compatibility condition (which is the same derived in [2] for the existence of a stationary solution having bounded and strictly positive density).

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Authors and Affiliations

  1. Matematický ústav ČSAV, Žitná 25, 115 67, Praha 1, Czechoslovakia

    Ivan Straškraba

  2. Dipartimento di Matematica, Università di Trento, 38050, Povo (Trento), Italy

    Alberto Valli

Authors
  1. Ivan Straškraba
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  2. Alberto Valli
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Straškraba, I., Valli, A. Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations. Manuscripta Math 62, 401–416 (1988). https://doi.org/10.1007/BF01357718

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  • DOI: https://doi.org/10.1007/BF01357718

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