Global well posedness for some dispersive partial differential equations

by Tzirakis, Nikolaos I

In this thesis we study the global in time solutions of some dispersive partial differential equations (pdes). More precisely in this work we consider the nonlinear Schr�¶dinger equation, the generalized Korteweg de Vries equation, and the Klein-Gordon-Schr�¶dinger system. For these equations, a local in time solution is known to exist. Using a modified functional that is closely related to the original energy functional of the equations, we show how to iterate the local result and prove that the solutions exist for all time. Our proofs also demonstrate polynomial in time bounds on the solutions within an appropriate function space.