Vol. 1, No. 3, 2019

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Almost sure local well-posedness for the supercritical quintic NLS

Justin T. Brereton

Vol. 1 (2019), No. 3, 427–453
Abstract

This paper studies the quintic nonlinear Schrödinger equation on d with randomized initial data below the critical regularity H(d1)2 for d 3. The main result is a proof of almost sure local well-posedness given a Wiener randomization of the data in Hs 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.

Keywords
almost sure well-posedness, supercritical, dispersive, PDEs, NLS equation
Mathematical Subject Classification 2010
Primary: 35K55
Secondary: 35R60
Milestones
Received: 9 April 2018
Accepted: 19 June 2018
Published: 8 August 2018
Authors
Justin T. Brereton
Department of Mathematics
University of California
Berkeley, CA
United States