Wellposedness of some quasi-linear Schrodinger equations

作者：Chemin Jean Yves^*; Salort Delphine

来源：Science China Mathematics, 2015, 58(5): 891-914.

DOI：10.1007/s11425-015-4993-5

• quasilinear Schrodinger equation
• Strichartz estimates
• paradiffential calculus
• stationary phase method

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 and belonging to the Besov space . 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 norm on the initial data.

• 出版日期2015-5