On the Semi-classical Limit of Quantum Zakharov System

  • 張 惟傑

Student thesis: Master's Thesis

Abstract

In this thesis we mainly study the paper with title" Global well-posedness and the classical limit of the solution for the quantum Zakharov system" authored by Yanfeng Guo Jingjun Zhang and Boling Guo and elaborate the details of this work First the authors prove that the quantum Zakharov system with nice initial data admits a unique solution staying in a nice space for all time and the solution depends continuously on initial data In order to prove this result we use the solution formula of nonlinear Schrodinger equation and nonlinear wave equation and make use of the standard contraction method to get the existence and uniqueness of local solution And then we use the uniform bound estimate of the solution to extend it to global well-posedness Also the same result hold if the condition of initial data is relaxed Second with proper initial data we can use the energy estimate to get the classical limit for the system that is the quantum Zakharov system converges to the classical system as the the quantum parameter tends to zero Also the initial data can be relaxed for gettin the same result
Date of Award2016 Jul 7
Original languageEnglish
SupervisorYung-Fu Fang (Supervisor)

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