caa a22 4500 606193901 CHVBK 20210128100911.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00030-015-0339-9 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0339-9 Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type [Elektronische Daten] [Hakima Bessaih, Erika Hausenblas, Paul Razafimandimby] 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 $${\mathbb{R}^n}$$ 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- $${\alpha}$$ α 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. Springer Basel, 2015 Strong solution nationallicence Hydrodynamical systems nationallicence Navier-Stokes nationallicence MHD nationallicence Bénard convection nationallicence Boussinesq equations nationallicence Shell models nationallicence Leray- $${\alpha}$$ α nationallicence Levy noise nationallicence Poisson random measure nationallicence Bessaih Hakima Department of Mathematics, University of Wyoming, 1000 East University Avenue, 82071, Laramie, WY, USA aut Hausenblas Erika Department of Mathematics and Information Technology, Montanuniversität Leoben, Fr. Josefstr. 18, 8700, Leoben, Austria aut Razafimandimby Paul Department of Mathematics and Information Technology, Montanuniversität Leoben, Fr. Josefstr. 18, 8700, Leoben, Austria aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1661-1697 1021-9722 22:6<1661 2015 22 30 https://doi.org/10.1007/s00030-015-0339-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0339-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bessaih Hakima Department of Mathematics, University of Wyoming, 1000 East University Avenue, 82071, Laramie, WY, USA aut NATIONALLICENCE 700 1- Hausenblas Erika Department of Mathematics and Information Technology, Montanuniversität Leoben, Fr. Josefstr. 18, 8700, Leoben, Austria aut NATIONALLICENCE 700 1- Razafimandimby Paul Department of Mathematics and Information Technology, Montanuniversität Leoben, Fr. Josefstr. 18, 8700, Leoben, Austria aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1661-1697 1021-9722 22:6<1661 2015 22 30