On well-posedness of the initial boundary-value problem for the derivative nonlinear Schrödinger equation

This paper deals with an initial boundary-value problem for the generalized derivative nonlinear Schrödinger equation. The cases of zero Dirichlet and generalized periodic boundary conditions are considered. The global existence of a solution inL _∞(0,∞;H _b ¹) is proved. The uniqueness inL _∞(0,T;H _b ¹)∩{u: ?u/?x εL _∞(Ω×(0,T))} is also established.