Tunisian Journal of Mathematics

Almost sure local well-posedness for the supercritical quintic NLS

Justin T. Brereton

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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.

Article information

Source
Tunisian J. Math., Volume 1, Number 3 (2019), 427-453.

Dates
Received: 9 April 2018
Accepted: 19 June 2018
First available in Project Euclid: 15 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.tunis/1544842823

Digital Object Identifier
doi:10.2140/tunis.2019.1.427

Mathematical Reviews number (MathSciNet)
MR3907746

Zentralblatt MATH identifier
07027461

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Keywords
almost sure well-posedness supercritical dispersive PDEs NLS equation

Citation

Brereton, Justin T. Almost sure local well-posedness for the supercritical quintic NLS. Tunisian J. Math. 1 (2019), no. 3, 427--453. doi:10.2140/tunis.2019.1.427. https://projecteuclid.org/euclid.tunis/1544842823


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References

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