Well-posedness for the Cauchy problem associated to the Hirota-Satsuma equation: Periodic case

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:326

Article

Panthee, Mahendra ; Silva, Jorge Drumond

关键词: KdV equation;    Cauchy problem;    well-posedness;   

DOI  :  10.1016/j.jmaa.2006.03.010

来源: Elsevier

【 摘 要 】

We consider a system of Korteweg-de Vries (KdV) equations coupled through nonlinear terms, called the Hirota-Satsuma system. We study the initial value problem (IVP) associated to this system in the periodic case, for given data in Sobolev spaces H-s x Hs+l with regularity below the one given by the conservation laws. Using the Fourier transform restriction norm method, we prove local well-posedness whenever s > -1/2. Also, with some restriction on the parameters of the system, we use the recent technique introduced by Colliander et al., called I-method and almost conserved quantities, to prove global well-posedness for s > -3/14. (c) 2006 Elsevier Inc. All rights reserved.

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