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

Nako Hayashi, Keiichi Kato, Tohru Ozawa

Research output: Contribution to journalArticle

12 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 language English 273-285 13 Royal Society of Edinburgh - Proceedings A 126 2 Published - 1996 Yes

### Fingerprint

Benjamin-Ono Equation
Smoothing Effect
Hilbert Transform
Dilation

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

Dilation method and smoothing effects of solutions to the Benjamin-Ono equation. / Hayashi, Nako; Kato, Keiichi; Ozawa, Tohru.

In: Royal Society of Edinburgh - Proceedings A, Vol. 126, No. 2, 1996, p. 273-285.

Research output: Contribution to journalArticle

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