On the decaying property of quintic NLS on 3D hyperbolic space

In this paper, we study the (pointwise) decaying property of quintic NLS on the three-dimensional hyperbolic space H3. We show the nonlinear solution enjoys the same decay rate as the linear solution does. This result is based on the associated global well-posedness and scattering result in Ionescu...

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Bibliographic Details
Published in:Nonlinear analysis 2024-10, Vol.247, p.113599, Article 113599
Main Authors: Ma, Chutian, Wang, Han, Yu, Xueying, Zhao, Zehua
Format: Article
Language:English
Subjects:
Dispersive estimate
Fourth-order NLS
Hyperbolic space
Nonlinear Schrödinger equation
Scattering
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Summary:In this paper, we study the (pointwise) decaying property of quintic NLS on the three-dimensional hyperbolic space H3. We show the nonlinear solution enjoys the same decay rate as the linear solution does. This result is based on the associated global well-posedness and scattering result in Ionescu et al. (2012). This extends (Fan and Zhao, 2021)’ Euclidean works to the hyperbolic space with additional improvements in regularity requirement (lower and almost critical regularity assumed). Realizing such improvements also work for the Euclidean case, we obtain a result for the fourth-order NLS analogue studied in Yu et al. (2023) recently with better, i.e. almost critical regularity assumption.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2024.113599