On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations

Carlos E. Kenig, Kenneth D. Koenig

Type: Article

Publication Date: 2003-01-01

Citations: 151

DOI: https://doi.org/10.4310/mrl.2003.v10.n6.a13

Abstract

We prove that the Benjamin-Ono equation is locally well-posed in H s (R) for s > 9/8 and that for arbitrary initial data, the modified (cubic nonlinearity) Benjamin-Ono equation is locally well-posed in H s (R) for s ≥ 1.

Locations

Mathematical Research Letters - View - PDF

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+	Quelques généralisations de l'équation de Korteweg-de Vries, II	1979	Jean‐Claude Saut
+	Ill-Posedness Issues for the Benjamin--Ono and Related Equations	2001	Luc Molinet Jean‐Claude Saut Nikolay Tzvetkov
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+	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
+	Maximal Functions Associated to Filtrations	2001	Michael Christ Alexander Kiselev