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NCTS Seminar on PDE and Analysis
14:20 - 15:20, September 22, 2016 (Thursday)
Room 201, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 201室)
On the Quantum Zakharov System
Yung-fu Fang (National Cheng Kung University)

We will discuss some works on the quantum Zakharov system.First we discuss some local and global well-posedness problems,and the ill-posedness problem of the system. Then we investigate the adiabatic limit of the system which converges to a fourth order nonlinear Schr¨odinger equation. Finally we study the standing waves of the system and the related fourth order nonlinear Schr¨odinger equation, including the existence and stability of the standing waves. We will present three proofs for the existence of standing waves of the system. The first one is based on the notions of Nehari manifold and concentrated compactness, the second one is a perturbation of the ground state of the classical Zakharov system, the third one is an application of Lagrange multiplier.


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