On the propagation of regularities in solutions of the Benjamin-Ono equation

2014/09/08 by Pedro Isaza, Isaza, Pedro, Felipe Linares +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35Q53. Secondary: 35B05 #math.AP #msc:35B05 #msc:35Q53.

paper · pdf · doi:10.48550/arxiv.1409.2381

arxiv created 2014/09/08 · arxiv updated 2014/09/09

Abstract

We shall deduce some special regularity properties of solutions to the IVP associated to the Benjamin-Ono equation. Mainly, for datum u₀∈ H^3/2(\mathbb R) whose restriction belongs to H^m((b,∞)) for some m∈\mathbb Z⁺, m≥ 2, and b∈ \mathbb R we shall prove that the restriction of the corresponding solution u(⋅,t) belongs to H^m((β,∞)) for any β∈ \mathbb R and any t>0. Therefore, this type of regularity of the datum travels with infinite speed to its left as time evolves.

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