Blow-up Solutions for Mixed Nonlinear Schrödinger Equations

Tan, Shaobin

doi:10.1007/s10114-003-0295-x

Cited by 13 publications

(9 citation statements)

References 15 publications

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“…We also refer to [5] for a further numerical investigation of the structure of the singular profile near blowup times. Here, we also point out that negative energy solutions to DNLS on a bounded interval or on the half-line, with Dirichlet boundary conditions, blow up in finite time (see [42], [50]). …”

Section: Introductionmentioning

confidence: 84%

Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition inH12

Mosincat

2017

Journal of Differential Equations

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Abstract. We establish the global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in the Sobolev space H 1 2 , provided that the mass of initial data is less than 4π. This result matches the one by Miao, Wu, and Xu and its recent mass threshold improvement by Guo and Wu in the non-periodic setting. Below H 1 2 , we show that the uniform continuity of the solution map on bounded subsets of H s does not hold, for any gauge equivalent equation.

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Section: Introductionmentioning

confidence: 84%

Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition inH12

Mosincat

2017

Journal of Differential Equations

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“…Solutions of low regularity have been studied in [21], [3], [4], [13], [7]. The DNLS equation in a bounded domain Ω = (a, b) with zero Dirichlet boundary condition is studied in [5], [22]. There are only a few results for the equation (1.1) with general exponents σ > 0, as compared with σ = 1.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for a generalized derivative nonlinear Schrödinger equation

Hayashi¹,

Ozawa²

2016

Journal of Differential Equations

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“…Our main result states that global well-posedness of (1.1) in the periodic setting also holds with the same mass threshold 4π. [8,11].…”

Section: Introductionmentioning

confidence: 99%

A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle

Mosincat

2015

Comptes Rendus. Mathématique

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Presented by Haïm BrézisIn this note, we consider the derivative nonlinear Schrödinger equation on the circle. In particular, by adapting Wu's recent argument to the periodic setting, we prove its global well-posedness in H 1 (T), provided that the mass is less than 4π . Moreover, this mass threshold is independent of spatial periods.© 2015 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. r é s u m éOn considère dans cette note l'équation de Schrödinger avec dérivée sur le cercle. En particulier, en adaptant l'argument récent de Wu au cas periodique, on prouve que cette équation est globalement bien posée dans H 1 (T), pourvu que la masse soit inférieure à 4π . En outre, ce seuil pour la masse est indépendant des périodes spatiales.

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Blow-up Solutions for Mixed Nonlinear Schrödinger Equations

Cited by 13 publications

References 15 publications

Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition inH12

Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition inH12

Well-posedness for a generalized derivative nonlinear Schrödinger equation

A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle

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