一维二阶非线性薛定谔方程的局部适定性  

Local well-posedness of 1-D nonlinear second ordered schr?dinger equation

作　　者：向雅捷 Xiang Yajie(School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China)

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《湖南文理学院学报（自然科学版）》2017年第2期12-16,共5页Journal of Hunan University of Arts and Science(Science and Technology)

摘　　要：讨论了一维二阶非线性薛定谔方程在模空间M_(2,p)中的局部适定性问题,通过对频率进行一致分解,将解在全空间中的整体估计转化为单位区间中的局部估计;通过讨论不同频率间的相互关系,运用Strichartz估计和Bilinear Strichart估计得到方程的局部适定性。Local well-posedness problem is discussed.Through the frequency uniform decomposion of a solution inthe whole space,the global well-posedness estimate of the solution is converted into the unit local well-posednessestimate.By discussing the relationship between different frequency and using the Strichartz estimates and theBilinear Strichartz estimates,the local well-posedness of equation is obtained.

关 键 词：非线性薛定谔方程 局部适定性 低正则性 模空间 

分 类 号：O241.8[理学—计算数学]