GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H<sup>1</sup>(<b>R</b>)

Terence Tao

Type: Article

Publication Date: 2004-03-01

Citations: 225

DOI: https://doi.org/10.1142/s0219891604000032

Abstract

We show that the Benjamin–Ono equation is globally well-posed in H s (R) for s≥1. This is despite the presence of the derivative in the nonlinearity, which causes the solution map to not be uniformly continuous in H s for any s [18]. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.

Locations

Journal of Hyperbolic Differential Equations - View
arXiv (Cornell University) - PDF
Journal of Hyperbolic Differential Equations - View
arXiv (Cornell University) - PDF

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Works Cited by This (23)

Action	Title	Year	Authors
+ PDF	On the global well-posedness of the Benjamin-Ono equation	1991	Gustavo Ponce
+ PDF	Counterexamples to bilinear estimates related with the KdV equation and the nonlinear Schrödinger equation	2001	Kenji Nakanishi Hideo Takaoka Yoshio Tsutsumi
+ PDF	Smoothing properties of some weak solutions of the Benjamin-Ono equation	1990	Michael M. Tom
+	None	2001	Sergiù Klainerman Igor Rodnianski
+ PDF	Quadratic forms for the 1-D semilinear Schrödinger equation	1996	Carlos E. Kenig Gustavo Ponce Luis Vega
+	None	2001	Terence Tao
+	Space‐time estimates for null forms and the local existence theorem	1993	Sergiù Klainerman Matei Machedon
+	Ill-Posedness Issues for the Benjamin--Ono and Related Equations	2001	Luc Molinet Jean–Claude Saut Nikolay Tzvetkov
+	Smoothing properties and existence of solutions for the generalized Benjamin-Ono equation	1991	J. Ginibre G. Velo
+	On the cauchy problem for the benjamin-ono equation	1986	Rafael José Iório