%AStaffilani, Gigliola%AStaffilani, Gigliola [Department of Mathematics, MIT, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA]%AYu, Xueying%AYu, Xueying [Department of Mathematics, MIT, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA]%BJournal Name: Journal of Mathematical Physics; Journal Volume: 61; Journal Issue: 8; Related Information: CHORUS Timestamp: 2023-07-02 00:18:50 %D2020%IAmerican Institute of Physics %JJournal Name: Journal of Mathematical Physics; Journal Volume: 61; Journal Issue: 8; Related Information: CHORUS Timestamp: 2023-07-02 00:18:50 %K %MOSTI ID: 10186532 %PMedium: X %TOn the high–low method for NLS on the hyperbolic space %X

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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