The Library
Ill-posedness of the cubic nonlinear half-wave equation and other fractional NLS on the real line
Tools
Choffrut, Antoine and Pocovnicu, Oana (2017) Ill-posedness of the cubic nonlinear half-wave equation and other fractional NLS on the real line. International Mathematics Research Notes, 2018 (3). pp. 699-738. doi:10.1093/imrn/rnw246 ISSN 1073-7928.
PDF
1601.02000.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (389Kb) |
||
|
PDF
WRAP-ill-posedness-cubic-nonlinear-equation-Choffurt-2016.pdf - Accepted Version - Requires a PDF viewer. Download (724Kb) | Preview |
Official URL: https://doi.org/10.1093/imrn/rnw246
Abstract
In this paper, we study ill-posedness of cubic fractional nonlinear Schrödinger equations. First, we consider the cubic nonlinear half-wave equation (NHW) on R. In particular, we prove the following ill-posedness results: (i) failure of local uniform continuity of the solution map in Hs(R) for s∈(0,1/2), and also for s=0 in the focusing case; (ii) failure of C3- smoothness of the solution map in L2(R); (iii) norm inflation and, in particular, failure of continuity of the solution map in Hs(R), s<0. By a similar argument, we also prove norm inflation in negative Sobolev spaces for the cubic fractional NLS. Surprisingly, we obtain norm inflation above the scaling critical regularity in the case of dispersion |D|β with β>2.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QC Physics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Schrödinger equation | ||||||||
Journal or Publication Title: | International Mathematics Research Notes | ||||||||
Publisher: | Oxford University Press | ||||||||
ISSN: | 1073-7928 | ||||||||
Official Date: | 31 January 2017 | ||||||||
Dates: |
|
||||||||
Volume: | 2018 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 699-738 | ||||||||
DOI: | 10.1093/imrn/rnw246 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 1 November 2016 | ||||||||
Date of first compliant Open Access: | 24 December 2017 | ||||||||
Funder: | University of Edinburgh. Whittaker Research Fellowship, European Research Council (ERC), National Science Foundation (U.S.) (NSF) | ||||||||
Grant number: | Grant agreement no. 616797 (ERC), Grant no. DMS-1440140 (NSF) | ||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year