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On the well-posedness
problem for the derivative nonlinear Schrödinger equation
Rowan Killip, Maria Ntekoume and Monica Vişan |
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Vol. 16 (2023), No. 5, 1245–1270
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Abstract |
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We consider the derivative nonlinear Schrödinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and -critical with respect to scaling. We first discuss whether ensembles of orbits with -equicontinuous initial data remain equicontinuous under evolution. We prove that this is true under the restriction . We conjecture that this restriction is unnecessary. Further, we prove that the problem is globally well posed for initial data in under the same restriction on . Moreover, we show that this restriction would be removed by a successful resolution of our equicontinuity conjecture. |
Keywords
derivative nonlinear Schrödinger equation, well-posedness
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Mathematical Subject Classification
Primary: 35Q55
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Milestones
Received: 29 January 2021
Revised: 28 June 2021
Accepted: 6 October 2021
Published: 12 August 2023
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Authors |
| Rowan Killip | |
| Department of Mathematics University of California, Los Angeles Los Angeles, CA United States |
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| Maria Ntekoume | |
| Department of Mathematics Rice University Houston, TX United States |
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| Monica Vişan | |
| Math Sciences University of California, Los Angeles Los Angeles, CA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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