SPDE in Hilbert Space with Locally Monotone Coefficients

Details SPDE in Hilbert Space with Locally Monotone Coefficients SPDE in Hilbert Space with Locally Monotone Coefficients

2010-05-04

arxiv.org/abs/1005.0632v2

J. Funct. Anal. 259 (2010), 2902--2922

Mathematics

Probability

20 pages, add Remark 3.1 for stochastic Burgers equation

Scientific paper

10.1016/j.jfa.2010.05.012

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.

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