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Navier-stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case

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Abstract

We consider the equations which describe the motion of a viscous compressible fluid, taking into consideration the case of inflow and/or outflow through the boundary. By means of some a priori estimates we prove the existence of a global (in time) solution. Moreover, as a consequence of a stability result, we show that there exist a periodic solution and a stationary solution.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, I-38050, Povo (Trento), Italy

    Alberto Valli

  2. Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, PL-00-049, Warsaw, Poland

    Wojciech M. Zajaczkowski

Authors
  1. Alberto Valli
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  2. Wojciech M. Zajaczkowski
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Communicated by L. Nirenberg

Partially supported by G.N.A.F.A of C.N.R. (Italy)

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Valli, A., Zajaczkowski, W.M. Navier-stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case. Commun.Math. Phys. 103, 259–296 (1986). https://doi.org/10.1007/BF01206939

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  • DOI: https://doi.org/10.1007/BF01206939

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