Strong solutions for SPDE with locally monotone coefficients driven by L\'{e}vy noise

By Zdzisław Brzeźniak, Wei David Liu, Jiahui Zhu. 2011

142 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/2057e1d9c3596a9f09bf582eaa09ec1cc9ae620a

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Citations in the corpus

A Moderate Deviation Principle for 2-D Stochastic Navier-Stokes Equations Driven by Multiplicative L\'evy Noises (2015, background): “23) The following result follows by standard arguments (see [2], [21]).”
A moderate deviation principle for 2-D stochastic Navier-Stokes equations (2015, background): “23) The following result follows by standard arguments (see [2], [21]).”
Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, methodology): “Please see [54, 50, 25, 68] for SPDEs with generalized coercivity conditions or Lyapunov conditions, [10, 69, 42] for SPDEs driven by Levy noise, [27] for strong solutions to SPDEs of gradient type, [60, 79, 80] for multivalued and doubly stochastic partial differential equations, [62] for backward ”