Well-posedness and ill-posedness for the fourth order cubic nonlinear Schrödinger equation in negative Sobolev spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125342 ◽

2021 ◽

pp. 125342

Author(s):

Kihoon Seong

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Sobolev Spaces ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation ◽

Negative Sobolev Spaces

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Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces

Journal of Functional Analysis ◽

10.1016/j.jfa.2021.109150 ◽

2021 ◽

pp. 109150

Author(s):

Tadahiro Oh ◽

Kihoon Seong

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Sobolev Spaces ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Gaussian Measures ◽

Nonlinear Schrödinger ◽

Negative Sobolev Spaces

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Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in Lp-based Sobolev spaces

Journal of Mathematical Physics ◽

10.1063/5.0042321 ◽

2021 ◽

Vol 62 (7) ◽

pp. 071507

Author(s):

Benjamin Dodson ◽

Avraham Soffer ◽

Thomas Spencer

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Sobolev Spaces ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation

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Global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linear-nonlinear decomposition

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2013.33.1905 ◽

2013 ◽

Vol 33 (5) ◽

pp. 1905-1926 ◽

Cited By ~ 2

Author(s):

Benjamin Dodson ◽

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Nonlinear Decomposition ◽

Cubic Nonlinear Schrödinger Equation

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Global Well-Posedness of the Cubic Nonlinear Schrödinger Equation on Closed Manifolds

Communications in Partial Differential Equations ◽

10.1080/03605302.2011.642449 ◽

2012 ◽

Vol 37 (7) ◽

pp. 1186-1236 ◽

Cited By ~ 10

Author(s):

Zaher Hani

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation

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Global well-posedness for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space

Revista Matemática Iberoamericana ◽

10.4171/rmi/1295 ◽

2021 ◽

Author(s):

Benjamin Dodson

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Critical Space ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation

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Almost sure well-posedness of the cubic nonlinear Schrödinger equation below $L^{2}(\mathbb{T})$

Duke Mathematical Journal ◽

10.1215/00127094-1507400 ◽

2012 ◽

Vol 161 (3) ◽

pp. 367-414 ◽

Cited By ~ 39

Author(s):

James Colliander ◽

Tadahiro Oh

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation

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Almost sure well-posedness for the cubic nonlinear Schrödinger equation in the super-critical regime on $$\mathbb {T}^d$$, $$d\ge 3$$

Stochastic Partial Differential Equations Analysis and Computations ◽

10.1007/s40072-020-00183-6 ◽

2020 ◽

Author(s):

Haitian Yue

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Critical Regime ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation

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A Refined Well-Posedness for the Fourth-Order Nonlinear Schrödinger Equation Related to the Vortex Filament

Communications in Partial Differential Equations ◽

10.1080/03605300701629385 ◽

2007 ◽

Vol 32 (10) ◽

pp. 1493-1510 ◽

Cited By ~ 16

Author(s):

Zhaohui Huo ◽

Yueling Jia

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Vortex Filament ◽

Well Posedness ◽

Nonlinear Schrödinger

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Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces

Journal of Differential Equations ◽

10.1016/j.jde.2019.12.017 ◽

2020 ◽

Vol 269 (1) ◽

pp. 612-640

Author(s):

Tadahiro Oh ◽

Yuzhao Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Critical Spaces ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

The One ◽

Cubic Nonlinear Schrödinger Equation

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Global Well-posedness and Scattering for the Defocusing Cubic nonlinear Schrödinger equation in Four Dimensions

International Mathematics Research Notices ◽

10.1093/imrn/rnr051 ◽

2011 ◽

Vol 2012 (5) ◽

pp. 1037-1067 ◽

Cited By ~ 15

Author(s):

Monica Vişan

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Four Dimensions ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation

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