Wellposedness of some quasi-linear Schrdinger equations

作     者：CHEMIN Jean-Yves SALORT Delphine 

作者机构：Laboratoire J.-L. Lions UMR 7598 Universit'e Pierre et Marie Curie Laboratoire de Biologie Computationnelle et Quantitative UMR 7238Sorbonne Universit'es L'Institut Jacques Monod UMR 7592 Universit'e Paris Diderot 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2015年第58卷第5期

页      面：891-914页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation National Institutes of Health National Institute of Environmental Health Sciences(1452800) University of Kentucky 

主　　题：quasilinear Schrodinger equation Strichartz estimates paradiffential calculus stationary phase method 

摘      要：This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.