GLOBAL WELL-POSEDNESS FOR THE L-2-CRITICAL HARTREE EQUATION ON R-n, n >= 3

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We consider the initial value problem for the L-2-critical defocusing Hartree equation in R-n, n >= 3. We show that the problem is globally well posed in H-s(R-n) when 1 > s > 2(n-2)/3n-4. We use the "I-method" following [9] combined with a local in time Morawetz estimate for the smoothed out solution I phi as in [7].
Publisher
AMER INST MATHEMATICAL SCIENCES
Issue Date
2009
Language
English
Article Type
Article
Keywords

NONLINEAR SCHRODINGER-EQUATION; SCATTERING; DISPERSION; ENERGY

Citation

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.8, no.6, pp.1725 - 1743

ISSN
1534-0392
DOI
10.3934/cpaa.2009.8.1725
URI
http://hdl.handle.net/10203/97086
Appears in Collection
MA-Journal Papers(저널논문)
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