Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold

Abstract

In this article, we utilize the scale-invariant Strichartz estimate on waveguide which is developed recently by Barron \cite{Barron} based on Bourgain-Demeter $l^2$ decoupling method \cite{BD} to give a unified and simpler treatment of well-posedness results for energy critical nonlinear Schrödinger equation on waveguide when the whole dimension is three and four.

arXiv comment12 pages

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Cited by in corpus (1)

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