SPDE in Hilbert Space with Locally Monotone Coefficients

Abstract

In this paper we prove the existence and uniqueness of strong solutions for SPDE in Hilbert space with locally monotone coefficients, which is a generalization of the classical result of Krylov and Rozovskii for monotone coefficients. Our main result can be applied to different types of SPDEs such as stochastic reaction-diffusion equations, stochastic Burgers type equation, stochastic 2-D Navier-Stokes equation, stochastic $p$-Laplace equation and stochastic porous media equation with some non-monotone perturbations.

20 pages, add Remark 3.1 for stochastic Burgers equation

References in corpus (3)

• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Harnack inequality and applications for stochastic generalized porous media equations
• Rate of Convergence of Space Time Approximations for stochastic evolution equations

Cited by in corpus (5)

• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Local and global well-posedness of SPDE with generalized coercivity conditions
• Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions
• Impact of noise on parabolic equations
• Necessary Conditions for Optimal Control of SPDE with locally monotone coefficients