On Quantum Zakharov System in One Spatial Dimension

Abstract

In this dissertation we research some topics about the quantum Zakharov system in one spatial dimension and the topics including local well-posedness ill-posedness global wellposedness and semi-classical limit problems In addition we get the Strichartz estimates for the solutions of fourth-order Schr?dinger equation and fourth-order wave equation Some topics have been extensively studied for Zakharov system To obtain new results of related topics for the quantum Zakharov system we appropriately modify some methods and techniques which applied to the Zakharov system by Ginibre Tsutsumi and Velo [14] Holmer [18] Colliander Holmer and Tzirakis [6] and Guo Zhang and Guo [16] For the local well-posedness of quantum Zakharov system we get a larger region than Jiang Lin and Shao [20] Then we establish two results about the ill- posedness of quantum Zakharov system outside of the local well-posedness region Next we prove the global well-posedness of quantum Zakharov system with L2-Schr?dinger data As the quantum parameter tends to zero we formally get the result of Colliander Holmer and Tzirakis [6] for the Zakharov system We also consider the semi-classical limit for the quantum Zakharov system and the Zakharov system and improve the result of Guo Zhang and Guo [16]

Date of Award	2017 Jul 26
Original language	English
Supervisor	Yung-Fu Fang (Supervisor)