Differential and Integral Equations

KdV and BO equations with bore-like data

R. Iorio, F. Linares, and M. Scialom

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The global well-posedness of the initial-value problem associated to the Korteweg-de Vries equation with bore-like data is studied. In particular, we show that in the Sobolev space $H^s$, $s\ge 2$, the solutions of this problem remain bounded for any time. We also establish similar results for solutions of the initial-value problem associated to the Benjamin-Ono equation with this kind of data.

Article information

Differential Integral Equations, Volume 11, Number 6 (1998), 895-915.

First available in Project Euclid: 30 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]


Iorio, R.; Linares, F.; Scialom, M. KdV and BO equations with bore-like data. Differential Integral Equations 11 (1998), no. 6, 895--915. https://projecteuclid.org/euclid.die/1367329482

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