A Scattering Result of the Radial Cubic Defocusing Schr\"odinger Equation on the 3d Hyperbolic Space
Abstract
In this paper, we study the defocusing cubic Schr\"odinger equation on three dimensional hyperbolic space H3 with radial initial data in the Sobolev Space Hs(0<s<1). Our main result is that the initial value problem is globally wellposed and scatters for 1516<s<1. This is an extension of the work of Staffilani and Yu to the three dimensional hyperbolic space.
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