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24 June 2024
 
  » arxiv » 2302.00249

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On the growth of high Sobolev norms of the cubic nonlinear Schr"odinger equation on $mathbb{R} imes mathbb{T}$
Mingming Deng ; Kailong Yang ;
Date 1 Feb 2023
AbstractWe consider the cubic nonlinear Schr"odinger equation on product manifolds $mathbb{R} imes mathbb{T}$. In this paper, we obtain polynomial bounds on the growth in time of high Sobolev norms of the solutions. The main ingredient of the proof is to establish an iteration bound, which is based on the idea used by Bourgain in cite{B1}.
Source arXiv, 2302.00249
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