Tunisian Journal of Mathematics
- Tunisian J. Math.
- Volume 1, Number 3 (2019), 427-453.
Almost sure local well-posedness for the supercritical quintic NLS
This paper studies the quintic nonlinear Schrödinger equation on with randomized initial data below the critical regularity for . The main result is a proof of almost sure local well-posedness given a Wiener randomization of the data in for . 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.
Tunisian J. Math., Volume 1, Number 3 (2019), 427-453.
Received: 9 April 2018
Accepted: 19 June 2018
First available in Project Euclid: 15 December 2018
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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