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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Information Technology, Montan University Leoben, Franz Josef Str. 18, 8700, Leoben, Austria

    E. Hausenblas & P. A. Razafimandimby

  2. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Pretoria, 0002, South Africa

    P. A. Razafimandimby & M. Sango

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  1. E. Hausenblas
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  2. P. A. Razafimandimby
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  3. M. Sango
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Hausenblas, E., Razafimandimby, P.A. & Sango, M. Martingale Solution to Equations for Differential Type Fluids of Grade Two Driven by Random Force of Lévy Type. Potential Anal 38, 1291–1331 (2013). https://doi.org/10.1007/s11118-012-9316-7

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