Functions operating on modulation spaces and nonlinear dispersive equations (vol 270, pg 621, 2016)

作     者：Bhimani, Divyang G. Ratnakumar, P. K. 

作者机构：Harish Chandra Res Inst Allahabad 211019 Uttar Pradesh India 

出 版 物：《JOURNAL OF FUNCTIONAL ANALYSIS》 (函数分析杂志)

年 卷 期：2016年第270卷第6期

页      面：2375-2375页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Nonlinear operation Modulation spaces Dispersive equation Local well-posedness 

摘      要：The aim of this paper is two fold. We show that if a complex function F on CC operates in the modulation spaces Mp,1(Rn)Mp,1(Rn) by composition, then F is real analytic on R2≈CR2≈C. This answers negatively, the open question posed in Ruzhansky et al. (2012) [21], regarding the general power type nonlinearity of the form |u|αu|u|αu. We also characterise the functions that operate in the modulation space M1,1(Rn)M1,1(Rn).The local well-posedness of the NLS, NLW and NLKG equations for the ‘real entire’ nonlinearities are also studied in some weighted modulation spaces Msp,q(Rn).