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Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type

  • Hakima Bessaih
  • Erika Hausenblas
  • Paul André Razafimandimby
Article

Abstract

In this paper we prove the existence and uniqueness of maximal strong (in PDE sense) solution to several stochastic hydrodynamical systems on unbounded and bounded domains of \({\mathbb{R}^n}\), n = 2, 3. This maximal solution turns out to be a global one in the case of 2D stochastic hydrodynamical systems. Our framework is general in the sense that it allows us to solve the Navier–Stokes equations, MHD equations, Magnetic Bénard problems, Boussinesq model of the Bénard convection, Shell models of turbulence and the Leray-\({\alpha}\) model with jump type perturbation. Our goal is achieved by proving general results about the existence of maximal and global solution to an abstract stochastic partial differential equations with locally Lipschitz continuous coefficients. The method of the proofs are based on some truncation and fixed point methods.

Mathematics Subject Classification

60H15 35Q35 60H30 35R15 

Keywords

Strong solution Hydrodynamical systems Navier–Stokes MHD Bénard convection Boussinesq equations Shell models Leray-\({\alpha}\) Levy noise Poisson random measure 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Hakima Bessaih
    • 1
  • Erika Hausenblas
    • 2
  • Paul André Razafimandimby
    • 2
  1. 1.Department of MathematicsUniversity of WyomingLaramieUSA
  2. 2.Department of Mathematics and Information TechnologyMontanuniversität LeobenLeobenAustria

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