A Scattering Result of the Radial Cubic Defocusing Schrödinger Equation on the 3d Hyperbolic Space

Chutian Ma

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arXiv · 2210.13760

A Scattering Result of the Radial Cubic Defocusing Schrödinger Equation on the 3d Hyperbolic Space

Chutian Ma

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Abstract

In this paper, we study the defocusing cubic Schrödinger equation on three dimensional hyperbolic space $\mathbb{H}^3$ with radial initial data in the Sobolev Space $H^s(0<s<1)$. Our main result is that the initial value problem is globally wellposed and scatters for $\frac{15}{16}<s<1$. This is an extension of the work of Staffilani and Yu to the three dimensional hyperbolic space.

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Chutian Ma. 2022-10-26. A Scattering Result of the Radial Cubic Defocusing Schrödinger Equation on the 3d Hyperbolic Space. https://arxiv.org/abs/2210.13760

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