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Archive for Rational Mechanics and Analysis

, Volume 165, Issue 3, pp 243–269 | Cite as

Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

  • JOSEF MÁLEK
  • JINDŘICH NEČAS
  • K. R. RAJAGOPAL

Abstract

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships.

Keywords

Viscosity Weak Solution Large Class Existence Result Global Existence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • JOSEF MÁLEK
    • 1
  • JINDŘICH NEČAS
    • 2
  • K. R. RAJAGOPAL
    • 3
  1. 1.Mathematical Institute of Charles University, Sokolovská 83, 186 75 Prague 8, Czech RepublicCZ
  2. 2.Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USAUS
  3. 3.Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USAUS

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