Global existence versus finite time blowup dichotomy for the system of nonlinear Schrodinger equations

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We construct an extremizer for the Lieb-Thirring energy inequality (except the endpoint cases) developing the concentration-compactness technique for operator valued inequality in the formulation of the profile decomposition. Moreover, we investigate the properties of the extremizer, such as the system of Euler-Lagrange equations, regularity and summability. As an application, we study a dynamical consequence of a system of nonlinear Schrodinger equations with focusing cubic nonlinearities in three dimension when each wave function is restricted to be orthogonal. Using the critical element of the Lieb-Thirring inequality, we establish a global existence versus finite time blowup dichotomy. This result extends the single particle result of Holmer-Roudenko [35] to infinitely many particles system. (C) 2018 Elsevier Masson SAS. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2019-05
Language
English
Article Type
Article
Citation

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v.125, pp.283 - 320

ISSN
0021-7824
DOI
10.1016/j.matpur.2018.12.003
URI
http://hdl.handle.net/10203/262111
Appears in Collection
MA-Journal Papers(저널논문)
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