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2019 Almost sure local well-posedness for the supercritical quintic NLS
Justin T. Brereton
Tunisian J. Math. 1(3): 427-453 (2019). DOI: 10.2140/tunis.2019.1.427

Abstract

This paper studies the quintic nonlinear Schrödinger equation on d with randomized initial data below the critical regularity H ( d 1 ) 2 for d 3 . The main result is a proof of almost sure local well-posedness given a Wiener randomization of the data in H s for s ( 1 2 ( d 2 ) , 1 2 ( d 1 ) ) . The argument further develops the techniques introduced in the work of Á. Bényi, T. Oh and O. Pocovnicu on the cubic problem. The paper concludes with a condition for almost sure global well-posedness.

Citation

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Justin T. Brereton. "Almost sure local well-posedness for the supercritical quintic NLS." Tunisian J. Math. 1 (3) 427 - 453, 2019. https://doi.org/10.2140/tunis.2019.1.427

Information

Received: 9 April 2018; Accepted: 19 June 2018; Published: 2019
First available in Project Euclid: 15 December 2018

zbMATH: 07027461
MathSciNet: MR3907746
Digital Object Identifier: 10.2140/tunis.2019.1.427

Subjects:
Primary: 35K55
Secondary: 35R60

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.1 • No. 3 • 2019
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