Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.05.031 ◽

2007 ◽

Vol 328 (1) ◽

pp. 58-83 ◽

Author(s):

Chengchun Hao ◽

Ling Hsiao ◽

Baoxiang Wang

Keyword(s):

Cauchy Problem ◽

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 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 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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On the Cauchy problem of fourth-order nonlinear Schrödinger equations

Nonlinear Analysis ◽

10.1016/j.na.2006.04.020 ◽

2007 ◽

Vol 66 (12) ◽

pp. 2911-2930 ◽

Author(s):

Ai Guo ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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Global well-posedness and scattering for the focusing energy-critical nonlinear Schrödinger equations of fourth order in the radial case

Journal of Differential Equations ◽

10.1016/j.jde.2008.11.011 ◽

2009 ◽

Vol 246 (9) ◽

pp. 3715-3749 ◽

Author(s):

Changxing Miao ◽

Guixiang Xu ◽

Lifeng Zhao

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Radial Case ◽

Nonlinear Schrodinger Equations

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On the well-posedness of the Cauchy problem for some nonlocal nonlinear Schrödinger equations

Nonlinearity ◽

10.1088/1361-6544/aa6aad ◽

2017 ◽

Vol 30 (6) ◽

pp. 2308-2333 ◽

Author(s):

John Albert ◽

Estapraq Kahlil

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem ◽

Nonlocal Nonlinear

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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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Asymptotics for a class of oscillating fourth-order nonlinear Schrödinger equations

Journal of Mathematical Physics ◽

10.1063/1.5031825 ◽

2018 ◽

Vol 59 (7) ◽

pp. 071511

Author(s):

T. Saanouni

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

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 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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