Non-integer power estimate in modulation spaces and its applications

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 1443-1460
• 页数: 18页
• 语种: 英文
• DOI: 10.1007/s11425-016-9023-y

摘要

We give a method to estimate non-integer power function |u|ku in modulation space which is an open question in the study of modulation space.As an application,we can study Cauchy problem for the nonlinear Klein-Gordon equation with nonlinear term |u|ku in modulation space,where k is not an integer.Moreover,we also study the global solution with small initial value for the Klein-Gordon-Hartree equation.The results show some advantages of modulation space both in high and low regularity cases.