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

Abstract

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 Lévy 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.

44 pages, more examples are added as application of the main results

References in corpus (4)

• Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Local and global well-posedness of SPDE with generalized coercivity conditions
• Stochastic nonlinear beam equations driven by compensated Poisson random measures

Cited by in corpus (6)

• Local and global well-posedness of SPDE with generalized coercivity conditions
• Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators
• A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump Noise
• Semilinear Stochastic Evolution Equations with Lévy Noise and Monotone Nonlinearity
• Stochastic Evolution Equations with Multiplicative Poisson Noise and Monotone Nonlinearity: A New Approach
• Ergodicity of the 2D Navier-Stokes Equations with Degenerate Multiplicative Noise