English

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 pp-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

R2 v1 2026-06-21T15:18:35.062Z