On the high–low method for NLS on the hyperbolic space
Name
2004.05711.pdf
Description
Submitted version
Size
897.46 KB
Format
Adobe PDF
Checksum (MD5)
fce687da7e4c4c8e8057f3453a5e2c79
Author(s)
Staffilani, Gigliola
Yu, Xueying
Date Issued
2020
Journal
Journal of Mathematical Physics
Publisher
AIP Publishing
Version
Original manuscript
Abstract
© 2020 Author(s). In this paper, we first prove that the cubic, defocusing nonlinear Schrödinger equation on the two dimensional hyperbolic space with radial initial data in Hs(H2) is globally well-posed and scatters when s > 3/4. Then, we extend the result to nonlinearities of order p > 3. The result is proved by extending the high-low method of Bourgain in the hyperbolic setting and by using a Morawetz type estimate proved by Staffilani and Ionescu.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1063/5.0012061
