All Physics Faculty Publications

Title

Global existence for a system of Schrodinger equations with power-type nonlinearities

Document Type

Article

Journal/Book Title/Conference

Journal of Mathematical Physics

Volume

54

Issue

1

Publisher

American Institute of Physics

Publication Date

1-2013

DOI

doi.org/10.1063/1.4774149

Abstract

In this manuscript, we consider the Cauchy problem for a Schrödinger system with power-type nonlinearities. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of a vector-valued Gagliardo-Nirenberg inequality is deduced, which yields the minimal embedding constant for the inequality. Using this minimal embedding constant, global existence for small initial data is shown for the critical case p = 1 + 2/N. Finite-time blow-up, as well as stability of solutions in the critical case, is discussed.

Comments

Originally published by the American Institute of Physics (AIP) in the Journal of Mathematical Physics.

Link to publishers PDF below:

http://jmp.aip.org/resource/1/jmapaq/v54/i1/p011503_s1

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