Random attractors for locally monotone stochastic partial differential equations

Abstract

We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive Lévy noise. The main result is applicable to various types of SPDE such as stochastic Burgers type equations, stochastic 2D Navier-Stokes equations, the stochastic 3D Leray-α model, stochastic power law fluids, the stochastic Ladyzhenskaya model, stochastic Cahn-Hilliard type equations, stochastic Kuramoto-Sivashinsky type equations, stochastic porous media equations and stochastic p-Laplace equations.

Ergodicity for singular-degenerate porous media equations

“…A different approach to the long-time behaviour of solutions to SPDEs is to analyse the existence and the structure of random attractors of random dynamical systems, as e. g. in [16,15,23,26,10,27].…”