On well-posedness for the Benjamin-Ono equation

2005/09/05 by Nicolas Burq, Burq, N., Fabrice Planchon +1 · 3 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

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

openalex publication_date 2005/09/05 · 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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