On the Regularization Mechanism for the Periodic Korteweg-de Vries Equation

abstract

• 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 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 L2 we also show the Lipschitz-continuous dependence of these solutions with respect to the initial data as maps from s to s for s (-1,0]. 2010 Wiley Periodicals, Inc.

authors

• Titi, Edriss

published proceedings

• COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

author list (cited authors)

• Babin, A. V., Ilyin, A. A., & Titi, E. S.

citation count

• 61

complete list of authors

• Babin, Anatoli V||Ilyin, Alexei A||Titi, Edriss S

publication date

• May 2011

publisher

• Wiley  Publisher

published in

• Communications on Pure and Applied Mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics
• Brain Disorders

Digital Object Identifier (DOI)

• 10.1002/cpa.20356

start page

• 591

end page

• 648

volume

• 64

issue

• 5

URL

• http%3A%2F%2Fdx.doi.org%2F10.1002%2Fcpa.20356