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Global well-posedness
for the nonlinear Schrödinger equation with derivative in
energy space
Yifei Wu |
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Vol. 6 (2013), No. 8, 1989–2002
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Abstract |
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In this paper, we prove that there exists some small such that the derivative nonlinear Schrödinger equation (DNLS) is globally well-posed in the energy space, provided that the initial data satisfies . This result shows us that there are no blow-up solutions whose masses slightly exceed , even if their energies are negative. This phenomenon is much different from the behavior of the nonlinear Schrödinger equation with critical nonlinearity. The technique used is a variational argument together with the momentum conservation law. Further, for the DNLS on the half-line , we show the blow-up for the solution with negative energy. |
Keywords
nonlinear Schrödinger equation with derivative, global
well-posedness, blow-up, half-line
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Mathematical Subject Classification 2010
Primary: 35Q55
Secondary: 35A01, 35B44
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Milestones
Received: 9 March 2013
Revised: 11 September 2013
Accepted: 4 October 2013
Published: 20 April 2014
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Authors |
| Yifei Wu | |
| School of Mathematical Science Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing, 100875 China |
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