Vol. 5, No. 2, 2012

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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