Vol. 9, No. 3, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 10 issues

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
On the well-posedness of the generalized Korteweg–de Vries equation in scale-critical $\hat{L}^r$-space

Satoshi Masaki and Jun-ichi Segata

Vol. 9 (2016), No. 3, 699–725
Abstract

The purpose of this paper is to study local and global well-posedness of the initial value problem for the generalized Korteweg–de Vries (gKdV) equation in L̂r = {f S() : fL̂r = f̂Lr < }. We show (large-data) local well-posedness, small-data global well-posedness, and small-data scattering for the gKdV equation in the scale-critical L̂r-space. A key ingredient is a Stein–Tomas-type inequality for the Airy equation, which generalizes the usual Strichartz estimates for L̂r-framework.

Keywords
generalized Korteweg–de Vries equation, scattering problem
Mathematical Subject Classification 2010
Primary: 35Q53, 35B40
Secondary: 35B30
Milestones
Received: 28 July 2015
Revised: 17 November 2015
Accepted: 30 January 2016
Published: 17 June 2016
Authors
Satoshi Masaki
Laboratory of Mathematics
Institute of Engineering
Hiroshima University
Higashihiroshima, Hiroshima 739-8527
Japan
Jun-ichi Segata
Mathematical Institute
Tohoku University
6-3, Aoba, Aramaki, Aoba-ku
Sendai 980-8578
Japan