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arXiv · 2004.05711

On the high-low method for NLS on the hyperbolic space

Gigliola Staffilani·Xueying Yu
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Abstract

In this paper, we first prove that the cubic, defocusing nonlinear Schr\"odinger equation on the two dimensional hyperbolic space with radial initial data in $H^s(\mathbb{H}^2)$ is globally well-posed and scatters when $s > \frac{3}{4}$. Then we extend the result to nonlineraities 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 the first author and Ionescu.

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Gigliola Staffilani, Xueying Yu. 2020-04-12. On the high-low method for NLS on the hyperbolic space. https://doi.org/10.1063/5.0012061

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