On the high–low method for NLS on the hyperbolic space
© 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. Th...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/135430 |
| Summary: | © 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. |
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