Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise

Zdzisław Brzeźniak, Wei Liu, Jiahui Zhu

Published 2011-08-01, updated 2013-05-21Version 3

Motivated by applications to a manifold of semilinear and quasilinear stochastic partial differential equations (SPDEs) we establish the existence and uniqueness of strong solutions to coercive and locally monotone SPDEs driven by L\'{e}vy processes. We illustrate the main result of our paper by showing how it can be applied to various types of SPDEs such as stochastic reaction-diffusion equations, stochastic Burgers type equations, stochastic 2D hydrodynamical systems and stochastic equations of non-Newtonian fluids, which generalize many existing results in the literature.