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| In this talk we will first present some recent results on the well-posedness of SPDE with locally monotone coefficients, which generalize the classical results established by Pardoux, Krylov and Rozovskii etc. This extension provides a unified framework to analyze a large class of SPDEs such as stochastic Burgers type equations, stochastic 2D hydrodynamical systems, stochastic tamed 3D Navier-Stokes equations and stochastic equations of non-Newtonian fluids, which can not be included in the classical variational framework. The second part of this talk is to show the long time asymptotics of SPDE with locally monotone coefficients by proving the existence of random attractors. The approach is based on a construction of strictly stationary nonlinear Ornstein-Uhlenbeck processes, which also allows spatially much rougher noise than in existing works. |
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