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

2020/03/02 by Zhao, Zehua, Zheng, Jiqiang · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.00665

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 \citeBD 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>(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.

Cited by

• On Growth of Sobolev norms for cubic Schrödinger equation with harmonic potential in dimensions d=2,3

Related

• On the growth of Sobolev norm for the cubic NLS on two dimensional product space
• Global well-posedness and scattering for defocusing, cubic NLS in ℝ³
• Global solutions for 1D cubic defocusing dispersive equations: Part I
• Global well - posedness for the defocusing, cubic, nonlinear wave equation in three dimensions for radial initial in H^s × H^{s - 1}, s > (1)/(2)
• Global solutions for 1D cubic defocusing dispersive equations, Part IV: general dispersion relations