首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Continuous dependence for NLS in fractional order spaces
Authors:Thierry Cazenave  Daoyuan Fang
Institution:Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China
Abstract:For the nonlinear Schrödinger equation iutu+λα|u|u=0 in RN, local existence of solutions in Hs is well known in the Hs-subcritical and critical cases 0<α?4/(N−2s), where 0<s<min{N/2,1}. However, even though the solution is constructed by a fixed-point technique, continuous dependence in Hs does not follow from the contraction mapping argument. In this paper, we show that the solution depends continuously on the initial value in the sense that the local flow is continuous HsHs. If, in addition, α?1 then the flow is locally Lipschitz.
Keywords:primary  35Q55  secondary  35B30  46E35
本文献已被 ScienceDirect 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号