Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 07, pp. 1-20.
Global well-posedness of NLS-KdV systems for periodic functions
Carlos Matheus
Abstract:
We prove that the Cauchy problem of the
Schrodinger-Korteweg-deVries (NLS-KdV) system for
periodic functions is globally well-posed for initial
data in the energy space
.
More precisely, we
show that the non-resonant NLS-KdV system is globally well-posed for
initial data in
with s>11/13 and the resonant NLS-KdV system is globally well-posed
with s>8/9.
The strategy is to apply the I-method used by Colliander, Keel,
Staffilani, Takaoka and Tao. By doing this, we improve the
results by Arbieto, Corcho and Matheus concerning the global
well-posedness of NLS-KdV systems.
Submitted November 13, 2006. Published January 2, 2007.
Math Subject Classifications: 35Q55.
Key Words: Global well-posedness; Schrodinger-Korteweg-de Vries system;
I-method.
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Carlos Matheus
Instituto Nacional de Matemática Pura e Aplicada (IMPA)
Estrada Dona Castorina 110
Rio de Janeiro, 22460-320,
Brazil
email: matheus@impa.br |
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