Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2016.15.831 ◽

2016 ◽

Vol 15 (3) ◽

pp. 831-851 ◽

Author(s):

Hiroyuki Hirayama ◽

Mamoru Okamoto

Keyword(s):

Fourth Order ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Critical Regularity

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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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Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2010.27.1093 ◽

2010 ◽

Vol 27 (3) ◽

pp. 1093-1105 ◽

Author(s):

Jun-ichi Segata ◽

Keyword(s):

Fourth Order ◽

Standing Waves ◽

Type Equation ◽

Well Posedness ◽

Nonlinear Schrödinger

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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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Remark on well-posedness for the fourth order nonlinear Schrödinger type equation

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-04-07620-8 ◽

2004 ◽

Vol 132 (12) ◽

pp. 3559-3568 ◽

Author(s):

Jun-ichi Segata

Keyword(s):

Fourth Order ◽

Type Equation ◽

Well Posedness ◽

Nonlinear Schrödinger

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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 ◽

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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Well-posedness for a quadratic derivative nonlinear Schrödinger system at the critical regularity

Journal of Functional Analysis ◽

10.1016/j.jfa.2016.05.009 ◽

2016 ◽

Vol 271 (4) ◽

pp. 747-798 ◽

Author(s):

Masahiro Ikeda ◽

Nobu Kishimoto ◽

Mamoru Okamoto

Keyword(s):

Well Posedness ◽

Nonlinear Schrödinger ◽

Critical Regularity ◽

Nonlinear Schrödinger System ◽

Schrödinger System

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Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrödinger type equation on torus

Journal of Differential Equations ◽

10.1016/j.jde.2012.02.016 ◽

2012 ◽

Vol 252 (11) ◽

pp. 5994-6011 ◽

Author(s):

Jun-ichi Segata

Keyword(s):

Fourth Order ◽

Energy Inequality ◽

Type Equation ◽

Well Posedness ◽

Nonlinear Schrödinger

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Sharp well-posedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2018027 ◽

2018 ◽

Vol 17 (2) ◽

pp. 487-504

Author(s):

Yuanyuan Ren ◽

◽

Yongsheng Li ◽

Wei Yan ◽

Keyword(s):

Cauchy Problem ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

The Cauchy Problem

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Well-posedness of Initial Value Problem for Fourth Order Nonlinear Schrodinger Equation

Pure and Applied Mathematics Quarterly ◽

10.4310/pamq.2012.v8.n4.a11 ◽

2012 ◽

Vol 8 (4) ◽

pp. 1047-1074 ◽

Author(s):

Wenxu Ge ◽

Yu-Zhu Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Initial Value Problem ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Initial Value ◽

Nonlinear Schrödinger

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