A remark on global well-posedness below L^2 for the gKdV-3 equation

Mathematics – Analysis of PDEs

Scientific paper

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6 pages

Scientific paper

The I-method in its first version as developed by Colliander et al. is
applied to prove that the Cauchy-problem for the generalised Korteweg-de Vries
equation of order three (gKdV-3) is globally well-posed for large real-valued
data in the Sobolev space H^s, provided s>-1/42.

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