SPDE in Hilbert space with locally monotone coefficients

2010/05/31 by Wei Liu, Michael Röckner · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometry #Hilbert space #Mathematical analysis #Mathematics #Monotone polygon #Numerical methods in inverse problems #Pure mathematics #Reproducing kernel Hilbert space #Rigged Hilbert space #Space (punctuation) #Stability and Controllability of Differential Equations #Strongly monotone #math.AP #math.PR #msc:34D45 #msc:37L30 #msc:60H15

paper · pdf · doi:10.1016/j.jfa.2010.05.012

published as J. Funct. Anal. 259 (2010), 2902--2922 · 20 pages, add Remark 3.1 for stochastic Burgers equation

openalex publication_date 2010/06/02 · arxiv created 2010/10/22 · arxiv updated 2010/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations

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