Long time dynamics for defocusing cubic NLS on three dimensional product space
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 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 (Hs, s>56) 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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