On well-posedness for the Benjamin-Ono equation

2005/09/05 by N. Burq, Nicolas Burq, Burq, N. +3 · 4 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0509096

Important changes. We improved both existence and uniqueness results. In particular, uniqueness holds in the natural $L^\infty_t; H^{1/2}_x$ energy space

openalex publication_date 2005/09/05 · arxiv created 2005/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove existence of solutions for the Benjamin-Ono equation with data in H^s(\R), s>0. Thanks to conservation laws, this yields global solutions for H^\frac 1 2(\R) data, which is the natural ``finite energy'' class. Moreover, inconditional uniqueness is obtained in L^∞_t(H^\frac 1 2(\R)), which includes weak solutions, while for s>\frac 3 20, uniqueness holds in a natural space which includes the obtained solutions.

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