On the local well-posedness for some systems of coupled KdV equations

Abstract:

Using the theory developed by Kenig, Ponce, and Vega, we prove that the Hirota-Satsuma system is locally well-posed in Sobolev spaces Hs (R) × Hs (R) for 3 / 4 < s ≤ 1. We introduce some Bourgain-type spaces Xs, ba for a ≠ 0, s, b ∈ R to obtain local well-posedness for the Gear-Grimshaw system in Hs (R) × Hs (R) for s > - 3 / 4, by establishing new mixed-bilinear estimates involving the two Bourgain-type spaces Xs, b- α- and Xs, b- α+ adapted to ∂t + α- ∂x3 and ∂t + α+ ∂x3 respectively, where | α+ | = | α- | ≠ 0. © 2007 Elsevier Ltd. All rights reserved.

Año de publicación:

2008

Keywords:

• KdV equation
• Gear-Grimshaw system
• Hirota-Satsuma system

Fuente:

scopus