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Potential Analysis

, Volume 38, Issue 4, pp 1291–1331 | Cite as

Martingale Solution to Equations for Differential Type Fluids of Grade Two Driven by Random Force of Lévy Type

  • E. Hausenblas
  • P. A. Razafimandimby
  • M. Sango
Article

Abstract

In this article we study a system of nonlinear non-parabolic stochastic evolution equations driven by Lévy noise type. This system describes the motion of second grade fluids driven by random force. Global existence of a martingale solution is proved under general conditions on the noise. Since the coefficient of the noise does not satisfy a Lipschitz property, we could not prove any pathwise uniqueness result. We note that this is the first work dealing with a stochastic model for non-Newtonian fluids excited by external forces of Lévy noise type.

Keywords

Second grade fluid Lévy noise Stochastic partial differential equations Poisson random measure Non-Newtonian fluids 

Mathematics Subject Classifications (2010)

Primary 60H15 60J75 Secondary 60G44 60G55 76M35 

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • E. Hausenblas
    • 1
  • P. A. Razafimandimby
    • 1
    • 2
  • M. Sango
    • 2
  1. 1.Department of Mathematics and Information TechnologyMontan University LeobenLeobenAustria
  2. 2.Department of Mathematics and Applied MathematicsUniversity of PretoriaPretoriaSouth Africa

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