A decomposition for the Schrödinger equation with applications to bilinear and multilinear estimates

Felipe Hernandez

doi:10.3934/cpaa.2018034

Article Contents

2018, Volume 17, Issue 2: 627-646. Doi: 10.3934/cpaa.2018034

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A decomposition for the Schrödinger equation with applications to bilinear and multilinear estimates

Felipe Hernandez^,

182 Memorial Dr, Cambridge, MA 02142, USA

* Corresponding author:Felipe Hernandez
* Corresponding author:Felipe Hernandez

Received: November 30, 2015

Revised: August 31, 2017

Published: June 2018

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Abstract

A new decomposition for frequency-localized solutions to the Schrodinger equation is given which describes the evolution of the wavefunction using a weighted sum of Lipschitz tubes. As an application of this decomposition, we provide a new proof of the bilinear Strichartz estimate as well as the multilinear restriction theorem for the paraboloid.

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Mathematics Subject Classification: Primary:35Q41;Secondary:42B37.

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References

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