The Nonlinear Schrödinger Limit and The InitialLayer of The Zakharov Equations

• Main Authors: Wei-ChihMa, 馬偉智
• Other Authors: Yung-fu Fang
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/3k47rc

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 105 === We study the paper “The Nonlinear Schrödinger Limit and The Initial Layer of The Zakharov Equations”, by T. Ozawa and Y. Tsutsumi [18], in details and we elaborate the work in this report. The formation of the convergence of solutions for Zakharov equations as the ion sound speed goes to infinity is discussed. The decay rate of the solutions tending to the corresponding solutions for the nonlinear Schrödinger equation is given and they explain how the initial layer phenomena occur. A characterization is given of the relation between the convergence rate in and the formation of the initial layers. We present the details which is skipped in the paper and put in this thesis, we have revised some mistakes, including typos, in some formulas and in the proofs.