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Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise. (English) Zbl 1310.60091
Summary: Motivated by applications to various semilinear and quasi-linear stochastic partial differential equations (SPDEs) appeared in real world models, we establish the existence and uniqueness of strong solutions to coercive and locally monotone SPDEs driven by Lévy processes. We illustrate the main results of our paper by showing how they can be applied to a large class of SPDEs such as stochastic reaction-diffusion equations, stochastic Burger’s type equations, stochastic 2D hydrodynamical systems and stochastic equations of non-Newtonian fluids, which generalize many existing results in the literature.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G51 Processes with independent increments; Lévy processes
35R60 PDEs with randomness, stochastic partial differential equations
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