On the low regularity phase space of the Benjamin-Ono equation

2023/08/15 by Gérard, Patrick, Topalov, Peter
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.07829

Abstract

In this paper we prove that the Benjamin-Ono equation is globally in time C⁰-well-posed in the Hilbert space H^{-1/2,√(log)}(\mathbbT,ℝ) of periodic distributions in H^-1/2(\mathbbT,ℝ) with √(log)-weights. The space H^{-1/2,√(log)}(\mathbbT,ℝ) can thus be considered as a maximal low regularity phase space for the Benjamin-Ono equation corresponding to the scale H^s(\mathbbT,ℝ), s>-1/2.

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