Wellposedness of some quasi-linear Schrdinger equations  

作　　者：CHEMIN Jean-Yves SALORT Delphine 

机构地区：[1]Laboratoire J.-L. Lions, UMR 7598, Universit'e Pierre et Marie Curie [2]Laboratoire de Biologie Computationnelle et Quantitative, UMR 7238,Sorbonne Universit'es [3]L'Institut Jacques Monod, UMR 7592, Universit'e Paris Diderot

出　　处：《Science China Mathematics》2015年第5期891-914,共24页中国科学：数学（英文版）

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.This article is devoted to the study of a quasilinear Schrdinger 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˙B3/22,1. 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+ε2,∞norm on the initial data.

关 键 词：quasilinear Schrodinger equation Strichartz estimates paradiffential calculus stationary phase method 

分 类 号：O175[理学—数学]