Vol. 5, No. 2, 2012

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

Volume 12
Issue 8, 1891–2146
Issue 7, 1643–1890
Issue 7, 1397–1644
Issue 6, 1397–1642
Issue 5, 1149–1396
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

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
Editorial Board
Subscriptions
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
The Cauchy problem for the Benjamin–Ono equation in $L^2$ revisited

Luc Molinet and Didier Pilod

Vol. 5 (2012), No. 2, 365–395
Abstract

Ionescu and Kenig proved that the Cauchy problem associated with the Benjamin–Ono equation is globally well posed in L2(). In this paper we give a simpler proof of Ionescu and Kenig’s result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in Hs() for s > 1 4. Note that our approach also permits us to simplify the proof of the global well-posedness in L2(T) and yields unconditional well-posedness in H1 2 (T).

Keywords
Benjamin–Ono equation, initial value problem, gauge transformation
Mathematical Subject Classification 2010
Primary: 35A07, 35Q53
Secondary: 76B55
Milestones
Received: 7 September 2010
Accepted: 15 January 2011
Published: 27 August 2012
Authors
Luc Molinet
Laboratoire de Mathématiques et Physique Théorique
Université de Tours
Parc Grandmont
37200 Tours
France
Didier Pilod
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Caixa Postal 68530
21945-970 Rio de Janeiro
Brazil