The Well-posedness And Blowing Up Of Solutions For The Generalized Derivative Nonlinear Schr(?)dinger Equation

In this thesis,we mainly study the generalized derivative nonlinear Schr(?)dinger equation.The equation is derived from a model of Alfvén wave in plasma physics.By using the parabolic regularization theory,we discuss the local well-posedness of Hs-solutions of Cauchy problem,where s>3/2.For the initial boundary value problem,we use Yosida-type approximation method to prove the local well-posedness of H2-solutions.The process of constructing solution as a limit of approximate solutions is independent of a compactness argument.We also prove the global well-posedness of H1-weak solutions for the initial boundary value problem by the Galerkin's method.In addition,we obtain the existence and some properties of blow-up solutions when the initial value and parameters satisfy certain conditions.