Recent advances on Schr\"odinger equations with dissipative nonlinearities

We give a survey on recent developments on nonlinear Schr\"odinger equations with dissipative structure based on the authors' recent works.

[1]  J. Segata,et al.  Polynomial deceleration for a system of cubic nonlinear Schrödinger equations in one space dimension , 2022, Nonlinear Analysis.

[2]  Satoshi Masaki,et al.  Asymptotic behavior in time of solution to system of cubic nonlinear Schr"odinger equations in one space dimension , 2021, 2112.06427.

[3]  Takuya Sato.  Lower bound estimate for the dissipative nonlinear Schrödinger equation , 2021, Partial Differential Equations and Applications.

[4]  Y. Nishii.  Nondecay of the energy for a system of semilinear wave equations , 2020, Kyoto Journal of Mathematics.

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[6]  Takuya Sato.  $$L^2$$-decay estimate for the dissipative nonlinear Schrödinger equation in the Gevrey class , 2020, Archiv der Mathematik.

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[8]  Chunhua Li,et al.  On the derivative nonlinear Schrödinger equation with weakly dissipative structure , 2020, Journal of Evolution Equations.

[9]  G. Hoshino.  Asymptotic behavior for solutions to the dissipative nonlinear Schrödinger equations with the fractional Sobolev space , 2019, Journal of Mathematical Physics.

[10]  T. Cazenave,et al.  Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation , 2019, Discrete & Continuous Dynamical Systems - A.

[11]  Chunhua Li,et al.  Large Time Asymptotics for a Cubic Nonlinear Schrödinger System in One Space Dimension, II , 2019, Tokyo Journal of Mathematics.

[12]  Hideaki Sunagawa,et al.  On Agemi-type structural conditions for a system of semilinear wave equations , 2019 .

[13]  Hideaki Sunagawa,et al.  Small data global existence for a class of quadratic derivative nonlinear Schrödinger systems in two space dimensions , 2018, Journal of Differential Equations.

[14]  N. Hayashi,et al.  Upper and lower time decay bounds for solutions of dissipative nonlinear Schrödinger equations , 2017 .

[15]  F. Pusateri,et al.  Almost global existence for cubic nonlinear Schrödinger equations in one space dimension , 2016, 1605.03247.

[16]  Guangzhi Jin,et al.  The initial value problem for nonlinear Schrödinger equations with a dissipative nonlinearity in one space dimension , 2016 .

[17]  Chunhua Li,et al.  Remarks on derivative nonlinear Schr\"odinger systems with multiple masses , 2016, 1603.04966.

[18]  Chunhua Li,et al.  Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields , 2016 .

[19]  Hideaki Sunagawa,et al.  The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension , 2015, 1511.03126.

[20]  Chunhua Li,et al.  On Schrödinger systems with cubic dissipative nonlinearities of derivative type , 2015, 1507.07617.

[21]  Donghyun Kim,et al.  A note on decay rates of solutions to a system of cubic nonlinear Schrödinger equations in one space dimension , 2014, Asymptot. Anal..

[22]  M. Ikeda,et al.  Null Structure in a System of Quadratic Derivative Nonlinear Schrödinger Equations , 2013, 1305.3662.

[23]  Chunhua Li,et al.  A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D , 2013, Differential and Integral Equations.

[24]  Chunhua Li,et al.  Decay of solutions for a system of nonlinear Schrödinger equations in 2D , 2012 .

[25]  Hideaki Sunagawa.  The lifespan of solutions to nonlinear Schrödinger and Klein-Gordon equations , 2008 .

[26]  Nakao Hayashi,et al.  On the Schrödinger Equation with Dissipative Nonlinearities of Derivative Type , 2007, SIAM J. Math. Anal..

[27]  Akihiro Shimomura,et al.  Asymptotic Behavior of Solutions for Schrödinger Equations with Dissipative Nonlinearities , 2006 .

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[30]  T. Ogawa,et al.  L 2 -decay rate for the critical nonlinear Schr¨odinger equation with a small smooth data , 2020 .

[31]  G. Hoshino.  Dissipative nonlinear schrödinger equations for large data in one space dimension , 2020, Communications on Pure & Applied Analysis.

[32]  Y. Nakamura,et al.  Decay estimate and asymptotic behavior of small solutions to Schrödinger equations with subcritical dissipative nonlinearity , 2019 .

[33]  Akihiro Shimomura,et al.  Large time behavior of solutions to Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data , 2009 .

[34]  砂川 秀明.  Lower bounds of the lifespan of small data solutions to the nonlinear Schrödinger equations , 2005 .