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Local and global well-posedness of SPDE with generalized coercivity conditions. (English) Zbl 1264.60046
The authors establish the local and global existence and uniqueness of solutions to general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is obtained for stochastic evolution equations in Hilbert spaces with additive noise. As applications, the main results are applied to obtain simpler proofs in known cases as the stochastic 3D Navier-Stokes equation, the tamed 3D Navier-Stokes equation and the Cahn-Hilliard equation, but also to get new results for stochastic surface growth PDE and stochastic power law fluids.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35K55 Nonlinear parabolic equations
35Q30 Navier-Stokes equations
34G20 Nonlinear differential equations in abstract spaces
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