## Advances in Differential Equations

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

Clément Gallo

#### Abstract

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

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

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR2123133

Zentralblatt MATH identifier
1107.35099

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

#### Citation

Gallo, Clément. Korteweg-de Vries and Benjamin-Ono equations on Zhidkov spaces. Adv. Differential Equations 10 (2005), no. 3, 277--308.https://projecteuclid.org/euclid.ade/1355867880