Advances in Differential Equations

Korteweg-de Vries and Benjamin-Ono equations on Zhidkov spaces

Clément Gallo

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Motivated by the study of the Cauchy problem with bore-like initial data, we show the "well-posedness" for Korteweg-de Vries and Benjamin-Ono equations with initial data in Zhidkov spaces $X^s$, with respectively $s>1$ and $s>5/4$. Here, "well-posedness" includes local (global in some cases) existence, uniqueness under a supplementary assumption, and continuity with respect to the initial data.

Article information

Adv. Differential Equations, Volume 10, Number 3 (2005), 277-308.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35A05 35A07


Gallo, Clément. Korteweg-de Vries and Benjamin-Ono equations on Zhidkov spaces. Adv. Differential Equations 10 (2005), no. 3, 277--308.

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