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| The Cauchy Problem for Coupled Nonlinear Schrödinger Equations with Linear Damping: Local and Global Existence and Blowup of Solutions |
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Citation： |
Joāo-Paulo DIAS,Mário FIGUEIRA,Vladimir V. KONOTOP.The Cauchy Problem for Coupled Nonlinear Schrödinger Equations with Linear Damping: Local and Global Existence and Blowup of Solutions[J].Chinese Annals of Mathematics B,2016,37(5):665~682 |
| Page view： 1274
Net amount： 1192 |
Authors： |
Joāo-Paulo DIAS; Mário FIGUEIRA;Vladimir V. KONOTOP |
Foundation： |
This work was supported by the Funda\c{c}$\wt{\rm a}$o
para a Ci\^{e}ncia e Tecnologia (Portugal)
(Nos.PEst-OE/MAT/UI0209/2013, UID/MAT/04561/2013,
PTDC/FIS-OPT/1918/2012, UID/FIS/00618/2013) |
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| Abstract： |
The authors study, by applying and extending the methods developed
by Cazenave (2003), Dias and Figueira (2014), Dias et al. (2014),
Glassey (1994--1997), Kato (1987), Ohta and Todorova (2009) and
Tsutsumi (1984), the Cauchy problem for a damped coupled system of
nonlinear Schr\"odinger equations and they obtain new results on the
local and global existence of $H^{1}$-strong solutions and on their
possible blowup in the supercritical case and in a special
situation, in the critical or supercritical cases. |
Keywords： |
Nonlinear Schr\"odinger equations, Cauchy problem, Blowup of solutions, Dissipation |
Classification： |
35Q55, 33A05 |
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