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

Abstract

Motivated by applications to various semilinear and quasi-linear stochastic partial differential equations (SPDEs) appeared in real world models, we establish the existence and uniqueness of strong solutions to coercive and locally monotone SPDEs driven by Lévy processes. We illustrate the main results of our paper by showing how it can be applied to a large class 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.