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Low regularity global well-posedness for the nonlinear Schrödinger equation on closed manifolds
1. | Graduate School of Science and Engineering, Ehime University, 2-5 Bunkyo-cho, Matsuyama, 790-8577, Japan |
[1] |
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global well-posedness for a periodic nonlinear Schrödinger equation in 1D and 2D. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 37-65. doi: 10.3934/dcds.2007.19.37 |
[2] |
Zihua Guo, Yifei Wu. Global well-posedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 257-264. doi: 10.3934/dcds.2017010 |
[3] |
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global well-posedness for the $L^2$ critical nonlinear Schrödinger equation in higher dimensions. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1023-1041. doi: 10.3934/cpaa.2007.6.1023 |
[4] |
Chao Yang. Sharp condition of global well-posedness for inhomogeneous nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4631-4642. doi: 10.3934/dcdss.2021136 |
[5] |
Lassaad Aloui, Slim Tayachi. Local well-posedness for the inhomogeneous nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5409-5437. doi: 10.3934/dcds.2021082 |
[6] |
Benjamin Dodson. Global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linear-nonlinear decomposition. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1905-1926. doi: 10.3934/dcds.2013.33.1905 |
[7] |
Changxing Miao, Bo Zhang. Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 181-200. doi: 10.3934/dcds.2007.17.181 |
[8] |
Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa. Global well-posedness of critical nonlinear Schrödinger equations below $L^2$. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1389-1405. doi: 10.3934/dcds.2013.33.1389 |
[9] |
Yuanyuan Ren, Yongsheng Li, Wei Yan. Sharp well-posedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2018, 17 (2) : 487-504. doi: 10.3934/cpaa.2018027 |
[10] |
Jun-ichi Segata. Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1093-1105. doi: 10.3934/dcds.2010.27.1093 |
[11] |
Kelin Li, Huafei Di. On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4293-4320. doi: 10.3934/dcdss.2021122 |
[12] |
Boling Guo, Jun Wu. Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3749-3778. doi: 10.3934/dcdsb.2021205 |
[13] |
Shaoming Guo, Xianfeng Ren, Baoxiang Wang. Local well-posedness for the derivative nonlinear Schrödinger equation with $ L^2 $-subcritical data. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4207-4253. doi: 10.3934/dcds.2021034 |
[14] |
Massimo Cicognani, Michael Reissig. Well-posedness for degenerate Schrödinger equations. Evolution Equations and Control Theory, 2014, 3 (1) : 15-33. doi: 10.3934/eect.2014.3.15 |
[15] |
Tarek Saanouni. Global well-posedness of some high-order semilinear wave and Schrödinger type equations with exponential nonlinearity. Communications on Pure and Applied Analysis, 2014, 13 (1) : 273-291. doi: 10.3934/cpaa.2014.13.273 |
[16] |
Ademir Pastor. On three-wave interaction Schrödinger systems with quadratic nonlinearities: Global well-posedness and standing waves. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2217-2242. doi: 10.3934/cpaa.2019100 |
[17] |
Hiroyuki Hirayama, Mamoru Okamoto. Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity. Communications on Pure and Applied Analysis, 2016, 15 (3) : 831-851. doi: 10.3934/cpaa.2016.15.831 |
[18] |
Takeshi Wada. A remark on local well-posedness for nonlinear Schrödinger equations with power nonlinearity-an alternative approach. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1359-1374. doi: 10.3934/cpaa.2019066 |
[19] |
Hiroyuki Hirayama. Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1563-1591. doi: 10.3934/cpaa.2014.13.1563 |
[20] |
Chengchun Hao. Well-posedness for one-dimensional derivative nonlinear Schrödinger equations. Communications on Pure and Applied Analysis, 2007, 6 (4) : 997-1021. doi: 10.3934/cpaa.2007.6.997 |
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