Existence And Uniqueness Of Solutions For A Class Of Generalized Stochastic Evolution Equations

In this paper,we mainly study the existence and uniqueness of solutions for a class of generalized stochastic evolution equations under the variational framework.For a class of stochastic evolution equations with a degenerate operator,the generalized Ito formula with a degenerate operator is applied to make energy estimates.We prove the existence and uniqueness of solutions for stochastic evolution equations under local monotonicity condition by using weak convergence approach.After that,some exam-ples are given whose coefficients only satisfy local monotonicity condition,while the result of the classical monotonicity condition can not be applied.The content of the thesis is divided into four parts as follows:In Chapter 1,the background and related research progress of stochastic partial differential equations are presented.The main research results of this paper are also briefly introduced.In Chapter 2,some preliminary knowledge of the variational framework of the stochastic partial differential equation and the Ito formula are introduced.In Chapter 3,we prove the uniqueness and existence of solutions for a class of generalized stochastic evolution equations.In Chapter 4,we apply the main result to semilinear stochastic partial differential equation and stochastic 2D Navier-Stokes equation.