On the regularization mechanism for the periodic Korteweg–de Vries equation
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In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg-de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣs for s ≥ 0. Specifically, we prove the global existence, uniqueness, and Lipschitz-continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in L2 we also show the Lipschitz-continuous dependence of these solutions with respect to the initial data as maps from Ḣs to Ḣs for s ∈(-1,0]. © 2010 Wiley Periodicals, Inc.
author list (cited authors)
Babin, A. V., Ilyin, A. A., & Titi, E. S.