Journal
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume 64, Issue 5, Pages 591-648Publisher
WILEY-BLACKWELL
DOI: 10.1002/cpa.20356
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Funding
- AFOSR [FA9550-04-1-0359]
- Russian Foundation for Fundamental Research [09-01-00288, 08-01-00784]
- RAS [1]
- National Science Foundation [DMS-0708832]
- ISF [120/6]
- BSF [2004271]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [2004271] Funding Source: National Science Foundation
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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 (H) over dot(s) 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 L(2) we also show the Lipschitz-continuous dependence of these solutions with respect to the initial data as maps from (H) over dot(s) to (H) over dot(s) for s is an element of (-1; 0]. (C) 2010 Wiley Periodicals, Inc.
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