Local and global well-posedness of SPDE with generalized coercivity conditions

Abstract

In this paper we establish local and global existence and uniqueness of solutions for 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 space with general 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.

33 pages; correct some misprints

References in corpus (3)

• Global L_2-solutions of stochastic Navier-Stokes equations
• SPDE in Hilbert Space with Locally Monotone Coefficients
• Random attractors for a class of stochastic partial differential equations driven by general additive noise

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