Global well-posedness for the KP-II equation on the background of a non localized solution

Details Global well-posedness for the KP-II equation on the background of a non localized solution Global well-posedness for the KP-II equation on the background of a non localized solution

2010-10-19

arxiv.org/abs/1010.3996v1

Mathematics

Analysis of PDEs

Scientific paper

Motivated by transverse stability issues, we address the time evolution under the KP-II flow of perturbations of a solution which does not decay in all directions, for instance the KdV-line soliton. We study two different types of perturbations : perturbations that are square integrable in $ \R\times \T $ and perturbations that are square integrable in $ \R^2 $. In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.

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