On the existence of global solutions of the Hartree equation for initial data in the modulation space M<SUP>p</SUP>(qR)

作     者：Manna, Ramesh 

作者机构：Natl Inst Sci Educ & Res OCC Homi Bhabha Natl Inst Sch Math Sci Bhubaneswar 752050 India 

出 版 物：《JOURNAL OF DIFFERENTIAL EQUATIONS》 (微分方程杂志)

年 卷 期：2022年第317卷

页      面：70-88页

核心收录：

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

基　　金：DST-INSPIRE [DST/IN-SPIRE/04/2019/001914] 

主　　题：Non-linear Hartree equation Global well-posedness Modulation spaces 

摘      要：In this paper, we study the Cauchy problem for Hartree type equation iu(t) + u(xx) = [K * vertical bar u vertical bar(2)] with Cauchy data in modulation spaces Mp,q(R). We establish global well-posedness results in Mp,p (R) when K(x) = lambda/vertical bar x vertical bar(gamma), (lambda is an element of R, 0 gamma 1) with no smallness condition on initial data, where p is the Holder conjugate of p. Our proof uses a splitting method inspired by the work of Vargas-Vega, Hyakuna-Tsutsumi, Grunrock and Chaichenets et al. to the modulation space setting and exploits polynomial growth of the Schrodinger propagator on modulation spaces. (c) 2022 Elsevier Inc. All rights reserved.