Almost Global Existence for Cubic Nonlinear Schrödinger Equations in One Space Dimension
We consider non-gauge-invariant cubic nonlinear Schrödinger equations in one space dimension. We show that initial data of size ε in a weighted Sobolev space lead to solutions with sharp L∞x decay up to time exp(Cε-2). We also exhibit norm growth beyond this time for a specific choice of nonlinearity.
J. Murphy and F. Pusateri, "Almost Global Existence for Cubic Nonlinear Schrödinger Equations in One Space Dimension," Discrete and Continuous Dynamical Systems- Series A, vol. 37, no. 4, pp. 2077-2102, American Institute of Mathematical Sciences (AIMS), Apr 2017.
The definitive version is available at https://doi.org/10.3934/dcds.2017089
Mathematics and Statistics
Keywords and Phrases
Almost global existence; Cubic NLS; Method of space-time resonances
International Standard Serial Number (ISSN)
Article - Journal
© 2017 American Institute of Mathematical Sciences (AIMS), All rights reserved.
01 Apr 2017