SPDE in Hilbert Space with Locally Monotone Coefficients
Probability
2010-10-25 v2 Analysis of PDEs
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 -Laplace equation and stochastic porous media equation with some non-monotone perturbations.
Keywords
Cite
@article{arxiv.1005.0632,
title = {SPDE in Hilbert Space with Locally Monotone Coefficients},
author = {Wei Liu and Michael Röckner},
journal= {arXiv preprint arXiv:1005.0632},
year = {2010}
}
Comments
20 pages, add Remark 3.1 for stochastic Burgers equation