Large Deviation Principle For A Class Of Stochastic Evolution Equations With Locally Monotone Coefficients

In this paper,using the weak convergence approach,we prove the large deviation principle for a class of SPDEs with locally monotone coefficients under the extended variational framework.The main result obtained in this thesis not only covers some well-known results obtained in[16,38,52,56,58],but also can be applied to all SPDE models contained in[40].Then we can obtain the large deviation principle for a large class of SPDEs in Hydrodynamics and Mathematical Physics.We mainly use the stochastic control and weak convergence approach to prove the large deviation principle.We use the weak convergence approach to prove the Laplace principle,which is equivalent to the large deviation principle in our framework.In par-ticular,we do not assume the compactness of embeddings in the corresponding Gelfand triple(see[52])and the certain finite dimensional approximation of the diffusion coef-ficient(see[38]),but assume some regularity w.r.t.the time variable on the diffusion coefficient.