A lifespan estimate and a condition of the initial data for finite time blowup for the nonlinear Schrödinger equation are presented from a view point of ordinary differential equation (ODE) mechanism.
REFERENCES
1.
Cazenave
, T.
and Weissler
, F. B.
, “Some remarks on the nonlinear Schrödinger equation in the critical case
,” in Nonlinear Semigroups, Partial Differential Equations and Attractors (Washington, DC, 1987)
, Lecture Notes in Mathematics
Vol. 1394
(Springer
, Berlin
, 1989
), pp. 18
–29
.2.
Fujiwara
, K.
and Ozawa
, T.
, “Lifespan of strong solutions to the periodic nonlinear Schrödinger equation without gauge invariance
,” preprint.3.
Ikeda
, M.
and Inui
, T.
, “Small data blow-up of L2 or H1-solution for the semilinear Schrödinger equation without gauge invariance
,” J. Evol. Equations
15
, 571
–581
(2015
).4.
Ikeda
, M.
and Inui
, T.
, “Some non-existence results for the semilinear Schrödinger equation without gauge invariance
,” J. Math. Anal. Appl.
425
, 758
–773
(2015
).5.
Ikeda
, M.
and Wakasugi
, Y.
, “Small-data blow-up of L2-solution for the nonlinear Schrödinger equation without gauge invariance
,” Differ. Integr. Equations
26
, 1275
–1285
(2013
).6.
Oh
, T.
, “A blowup result for the periodic NLS without gauge invariance
,” C. R. Math. Acad. Sci. Paris
350
, 389
–392
(2012
).7.
Ozawa
, T.
and Yamazaki
, Y.
, “Life-span of smooth solutions to the complex Ginzburg-Landau type equation on a torus
,” Nonlinearity
16
, 2029
–2034
(2003
).8.
Tsutsumi
, Y.
, “L2-solutions for nonlinear Schrödinger equations and nonlinear groups
,” Funkcial. Ekvac.
30
, 115
–125
(1987
).9.
Zhang
, Q. S.
, “Blow-up results for nonlinear parabolic equations on manifolds
,” Duke Math. J.
97
, 515
–539
(1999
).10.
Zhang
, Q. S.
, “A blow-up result for a nonlinear wave equation with damping: The critical case
,” C. R. Acad. Sci. Paris Sér. I Math.
333
, 109
–114
(2001
).© 2016 Author(s).
2016
Author(s)
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