# American Institute of Mathematical Sciences

June  2018, 7(2): 275-280. doi: 10.3934/eect.2018013

## On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation

 1 Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri, 3, 56126 Pisa, Italy 2 Department of Applied Physics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

* Corresponding author: Kazumasa Fujiwara

The first author was partly supported by Grant-in-Aid for JSPS Fellows no 16J30008.

Received  May 2017 Revised  January 2018 Published  May 2018

An explicit lifespan estimate is presented for the derivative Schrödinger equations with periodic boundary condition.

Citation: Kazumasa Fujiwara, Tohru Ozawa. On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation. Evolution Equations & Control Theory, 2018, 7 (2) : 275-280. doi: 10.3934/eect.2018013
##### References:

show all references

The first author was partly supported by Grant-in-Aid for JSPS Fellows no 16J30008.

##### References:
 [1] Piero D'Ancona, Mamoru Okamoto. Blowup and ill-posedness results for a Dirac equation without gauge invariance. Evolution Equations & Control Theory, 2016, 5 (2) : 225-234. doi: 10.3934/eect.2016002 [2] Qihong Shi, Congming Peng, Qingxuan Wang. Blowup results for the fractional Schrödinger equation without gauge invariance. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021304 [3] Haixia Li. Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity. Evolution Equations & Control Theory, 2021, 10 (4) : 723-732. doi: 10.3934/eect.2020088 [4] Paweł Pilarczyk. Topological-numerical approach to the existence of periodic trajectories in ODE's. Conference Publications, 2003, 2003 (Special) : 701-708. doi: 10.3934/proc.2003.2003.701 [5] Xiaoliang Li, Baiyu Liu. Finite time blow-up and global solutions for a nonlocal parabolic equation with Hartree type nonlinearity. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3093-3112. doi: 10.3934/cpaa.2020134 [6] Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 [7] Grzegorz Karch, Kanako Suzuki, Jacek Zienkiewicz. Finite-time blowup of solutions to some activator-inhibitor systems. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 4997-5010. doi: 10.3934/dcds.2016016 [8] Thierry Cazenave, Yvan Martel, Lifeng Zhao. Finite-time blowup for a Schrödinger equation with nonlinear source term. Discrete & Continuous Dynamical Systems, 2019, 39 (2) : 1171-1183. doi: 10.3934/dcds.2019050 [9] Mickael Chekroun, Michael Ghil, Jean Roux, Ferenc Varadi. Averaging of time - periodic systems without a small parameter. Discrete & Continuous Dynamical Systems, 2006, 14 (4) : 753-782. doi: 10.3934/dcds.2006.14.753 [10] Hitoshi Ishii, Paola Loreti, Maria Elisabetta Tessitore. A PDE approach to stochastic invariance. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 651-664. doi: 10.3934/dcds.2000.6.651 [11] Yoshiki Maeda, Noboru Okazawa. Schrödinger type evolution equations with monotone nonlinearity of non-power type. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 771-781. doi: 10.3934/dcdss.2013.6.771 [12] Jong-Shenq Guo, Satoshi Sasayama, Chi-Jen Wang. Blowup rate estimate for a system of semilinear parabolic equations. Communications on Pure & Applied Analysis, 2009, 8 (2) : 711-718. doi: 10.3934/cpaa.2009.8.711 [13] Takeshi Wada. A remark on local well-posedness for nonlinear Schrödinger equations with power nonlinearity-an alternative approach. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1359-1374. doi: 10.3934/cpaa.2019066 [14] Yuzhu Han, Qi Li. Lifespan of solutions to a damped plate equation with logarithmic nonlinearity. Evolution Equations & Control Theory, 2022, 11 (1) : 25-40. doi: 10.3934/eect.2020101 [15] Junyong Eom, Ryuichi Sato. Large time behavior of ODE type solutions to parabolic $p$-Laplacian type equations. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4373-4386. doi: 10.3934/cpaa.2020199 [16] Alfonso C. Casal, Jesús Ildefonso Díaz, José M. Vegas. Finite extinction time property for a delayed linear problem on a manifold without boundary. Conference Publications, 2011, 2011 (Special) : 265-271. doi: 10.3934/proc.2011.2011.265 [17] Chiara Zanini, Fabio Zanolin. Periodic solutions for a class of second order ODEs with a Nagumo cubic type nonlinearity. Discrete & Continuous Dynamical Systems, 2012, 32 (11) : 4045-4067. doi: 10.3934/dcds.2012.32.4045 [18] Xuan Liu, Ting Zhang. Local well-posedness and finite time blowup for fourth-order Schrödinger equation with complex coefficient. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021156 [19] Menglan Liao. The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021025 [20] José Luis Bravo, Manuel Fernández, Antonio Tineo. Periodic solutions of a periodic scalar piecewise ode. Communications on Pure & Applied Analysis, 2007, 6 (1) : 213-228. doi: 10.3934/cpaa.2007.6.213

2020 Impact Factor: 1.081