On nonlinear Schrödinger equations with random initial data

Mathematics in Engineering ◽

10.3934/mine.2022030 ◽

2022 ◽

Vol 4 (4) ◽

pp. 1-14

Author(s):

Mitia Duerinckx ◽

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Keyword(s):

Initial Data ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Random Initial Data ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Spatially Homogeneous ◽

<abstract><p>This note is concerned with the global well-posedness of nonlinear Schrödinger equations in the continuum with spatially homogeneous random initial data.</p></abstract>

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On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite norm

Nonlinear Analysis ◽

10.1016/j.na.2010.10.003 ◽

2011 ◽

Vol 74 (4) ◽

pp. 1304-1319 ◽

Author(s):

Ryosuke Hyakuna ◽

Takamasa Tanaka ◽

Masayoshi Tsutsumi

Keyword(s):

Initial Data ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Large Initial Data ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

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Well-Posedness for a System of Quadratic Derivative Nonlinear Schrödinger Equations with Radial Initial Data

Annales Henri Poincaré ◽

10.1007/s00023-020-00931-3 ◽

2020 ◽

Vol 21 (8) ◽

pp. 2611-2636

Author(s):

Hiroyuki Hirayama ◽

Shinya Kinoshita ◽

Mamoru Okamoto

Keyword(s):

Initial Data ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2014.13.1563 ◽

2014 ◽

Vol 13 (4) ◽

pp. 1563-1591 ◽

Author(s):

Hiroyuki Hirayama

Keyword(s):

Initial Data ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Low Regularity ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Local well-posedness and smoothing effects of strongsolutions for nonlinear Schrödinger equations with potentials and magnetic fields

Hokkaido Mathematical Journal ◽

10.14492/hokmj/1285766208 ◽

2005 ◽

Vol 34 (1) ◽

pp. 37-63 ◽

Author(s):

Yoshihisa NAKAMURA ◽

Akihiro SHIMOMURA

Keyword(s):

Magnetic Fields ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Smoothing Effects ◽

Nonlinear Schrodinger Equations

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The well-posedness of nonlinear Schrödinger equations in Triebel-type spaces

Pacific Journal of Mathematics ◽

10.2140/pjm.2015.274.325 ◽

2015 ◽

Vol 274 (2) ◽

pp. 325-354

Author(s):

Shaolei Ru ◽

Jiecheng Chen

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

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Local well-posedness of the nonlinear Schrödinger equations on the sphere for data in modulation spaces

Communications in Partial Differential Equations ◽

10.1080/03605302.2015.1123274 ◽

2015 ◽

Vol 41 (4) ◽

pp. 732-747 ◽

Author(s):

Hideo Takaoka

Keyword(s):

Nonlinear Schrödinger Equations ◽

Modulation Spaces ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions d⩾9

Journal of Differential Equations ◽

10.1016/j.jde.2011.08.009 ◽

2011 ◽

Vol 251 (12) ◽

pp. 3381-3402 ◽

Author(s):

Changxing Miao ◽

Guixiang Xu ◽

Lifeng Zhao

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when $d = 2,3$ and $u_0$ is radial

Cambridge Journal of Mathematics ◽

10.4310/cjm.2019.v7.n3.a2 ◽

2019 ◽

Vol 7 (3) ◽

pp. 283-318

Author(s):

Benjamin Dodson

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2015.09.005 ◽

2016 ◽

Vol 105 (1) ◽

pp. 31-65 ◽

Author(s):

Michael Ruzhansky ◽

Baoxiang Wang ◽

Hua Zhang

Keyword(s):

Fourth Order ◽

Sobolev Spaces ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.03.055 ◽

2014 ◽

Vol 417 (2) ◽

pp. 580-600

Author(s):

Hayato Miyazaki

Keyword(s):

Initial Data ◽

Conservation Law ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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