Differential and Integral Equations

The Cauchy problem for Benney-Luke and generalized Benney-Luke equations

A. González N.

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Abstract

We examine the question of the minimal Sobolev regularity required to construct local solutions to the Cauchy problem for the Benney--Luke (BL) and generalized Benney--Luke (gBL) equations. As a consequence we prove that the initial-value problems are globally well-posed in the energy space.

Article information

Source
Differential Integral Equations Volume 20, Number 12 (2007), 1341-1362.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039069

Mathematical Reviews number (MathSciNet)
MR2377021

Zentralblatt MATH identifier
1212.35315

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 76B03: Existence, uniqueness, and regularity theory [See also 35Q35] 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]

Citation

González N., A. The Cauchy problem for Benney-Luke and generalized Benney-Luke equations. Differential Integral Equations 20 (2007), no. 12, 1341--1362. https://projecteuclid.org/euclid.die/1356039069.


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