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Long time dynamics for defocusing cubic NLS on three dimensional product space

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arxiv 2003.00665 v1 pith:WVJIUPNM submitted 2020-03-02 math.AP

Zehua Zhao , Jiqiang Zheng This is my paper · ORCID
classification math.AP
keywords cubicdefocusingdimensionalproductspacethreebilineardynamics
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abstract

In this article, we study long time dynamics for defocusing cubic NLS on three dimensional product space. First, we apply the decoupling method in Bourgain-Demeter \cite{BD} to establish a bilinear Strichartz estimate. Moreover, we prove global well-posedness for defocusing, cubic NLS on three dimensional product space with rough initial data ($H^s$, $s>\frac{5}{6}$) based on I-method and the bilinear estimate. At last, we discuss the growth of higher Sobolev norm problem which is tightly linked to the weak turbulence phenomenon.

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