On the Well-Posedness of a Class of Vector Schrödinger Equations

Advanced Nonlinear Studies ◽

10.1515/ans-2011-0303 ◽

2011 ◽

Vol 11 (3) ◽

Author(s):

Sara Barile ◽

Marco Squassina

Keyword(s):

Electromagnetic Field ◽

Schrodinger Equations ◽

Nonlocal Term ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrödinger Systems ◽

Schrödinger Systems ◽

Nonlocal Nonlinearities ◽

AbstractWe investigate the local and global well-posedness for a class of nonlinear Schrödinger systems with an external time independent electromagnetic field and nonlocal nonlinearities. New conditions related to the growth of the nonlocal term are detected which allow the solvability of the problem.

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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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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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Global well-posedness of critical nonlinear Schrödinger equations below $L^2$

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2013.33.1389 ◽

2013 ◽

Vol 33 (4) ◽

pp. 1389-1405 ◽

Author(s):

Yonggeun Cho ◽

◽

Gyeongha Hwang ◽

Tohru Ozawa ◽

◽

...

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise. Well-Posedness, Large Deviations and Support

Electronic Journal of Probability ◽

10.1214/ejp.v12-416 ◽

2007 ◽

Vol 12 (0) ◽

pp. 848-861 ◽

Author(s):

Eric Gautier

Keyword(s):

Large Deviations ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Fractional Noise ◽

Nonlinear Schrodinger Equations

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Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2007.6.997 ◽

2007 ◽

Vol 6 (4) ◽

pp. 997-1021 ◽

Author(s):

Chengchun Hao ◽

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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