Sharp thresholds of global existence and blowup for a system of Schroedinger equations with combined power-type nonlinearities

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3299309· OSTI ID:21335933

Xianfa, Song ^[1]

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1. Department of Mathematics, School of Science, Tianjin University, Tianjin 300072 (China)

In this paper, we consider the Cauchy problem of a nonlinear Schroedinger system. Through establishing a sharp weighted vector-valued Gagliardo-Nirenberg's inequality, we find that the best constant in this inequality can be regarded as the criterion of blowup and global existence of the solutions when p=4/N. And we prove that the solutions of this system will always exist globally if p<4/N. The sharp thresholds for blowup and global existence are also obtained when 4/N{<=}p<4/(N-2){sup +}.

• OSTI ID: 21335933
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 3; Other Information: DOI: 10.1063/1.3299309; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CAUCHY PROBLEM
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
SCHROEDINGER EQUATION
TETRAGONAL LATTICES
VECTORS