Modulation spaces and non-linear Hartree type equations

被引：5
|
作者：
Manna, Ramesh [1 ,2 ]
机构：
[1] Harish Chandra Res Inst, Sch Math, Allahabad 211019, Uttar Pradesh, India
[2] Homi Bhabha Natl Inst, Training Sch Complex, Bombay 400085, Maharashtra, India
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 162卷
关键词：
Hartree equation; Well-posedness; Modulation spaces; CAUCHY-PROBLEM; FOURIER MULTIPLIERS; SCHRODINGER-EQUATIONS; TIME;
D O I：
10.1016/j.na.2017.06.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the Cauchy problem for Hartree equation with cubic convolution nonlinearity F(u) = (k * vertical bar u vertical bar(2)) u under a specified condition on potential k with Cauchy data in modulation spaces M-p,M-q(R-n). We establish global well- posedness results in M-p,M-p(R-n) with 1 <= p < 2n/n+v, when k(x) = lambda/vertical bar x vertical bar(v) (lambda is an element of R, 0 < v < min{2, n/2}); in M-p,M-q(R-n) with 1 <= q <= p <= 2, when k is an element of M-infinity,M-1(R-n). (C) 2017 Elsevier Ltd. All rights reserved.
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页码：76 / 90
页数：15
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