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Abstract
In this article, we prove global wellposedness and scattering for the defocusing quintic nonlinear Schrodinger equation on the cylinder R × T in H1. We establish an infinite vectorvalued linear profile decomposition in L2 xhα , 0 < α ≤ 1, motivated by the linear profile decomposition of the masscritical Schrodinger equation in L2(Rd), d ≥ 1. Then by using the solution of the onediscretecomponent quintic resonant nonlinear Schrodinger system, whose scattering can be proved by using the techniques established by Dodson, to approximate the nonlinear profile, we can prove scattering in H1 by using the concentration compactness/rigidity method. As a byproduct of our proof of the scattering of the onediscretecomponent quintic resonant nonlinear Schrodinger system, we also prove the scattering conjecture for the twodiscretecomponent quintic resonant nonlinear Schrodinger system presented by Hani and Pausader in [Comm. Pure Appl. Math., 67 (2014), pp. 14661542].
Original language  English 

Pages (fromto)  41854237 
Number of pages  53 
Journal  SIAM Journal on Mathematical Analysis 
Volume  52 
Issue number  5 
DOIs  
Publication status  Published  2020 
Keywords
 Interaction Morawetz estimate
 Long time Strichartz estimate
 Nonlinear Schrodinger equation
 Profile decomposition
 Quintic resonant nonlinear Schrodinger system
 Scattering
 Wellposedness
Projects
 1 Active

Nonlinear harmonic analysis and dispersive partial differential equations
Sikora, A., Guo, Z., Hauer, D. & Tacy, M.
8/04/20 → 31/12/22
Project: Research