Dilation method and smoothing effects of solutions to the Benjamin-Ono equation

Nako Hayashi, Keiichi Kato, Tohru Ozawa

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13 Citations (Scopus)

Abstract

In this paper we study smoothing effects of solutions to the Benjamin-Ono equation (Formula Presented) where H is the Hilbert transform defined by Hf)(x) = p.v. 1/π ∫ f(y)/x - y dy. We prove that if φ ∈ H4 and (x∂x)4φ, then the solution u of (BO) belongs to Lloc (ℝ\{0}; H8, -4), where Hm,s = {f ∈ L2; ∥ (1 + x2)s/2(1 - ∂x 2f ∥ L2 < ∞}.

Original languageEnglish
Pages (from-to)273-285
Number of pages13
JournalRoyal Society of Edinburgh - Proceedings A
Volume126
Issue number2
Publication statusPublished - 1996
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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