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Nonlinear PDEs with modulated dispersion II: Korteweg–de Vries equation

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Date
2014
Publisher city
Paris
Publisher
Université Paris-Dauphine
Link to item file
http://arxiv.org/pdf/1406.7675.pdf
Dewey
Probabilités et mathématiques appliquées
Sujet
Regularization by noise phenomenon; Korteweg- de Vries equation; I-method; Controlled paths; Young integrals; Dispersion management
URI
https://basepub.dauphine.fr/handle/123456789/13741
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  • CEREMADE : Publications
Metadata
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Author
Gubinelli, Massimiliano
Chouk, Khalil
Type
Document de travail / Working paper
Item number of pages
37
Abstract (EN)
We continue the study of various nonlinear PDEs under the effect of a time–inhomogeneous and irregular modulation of the dispersive term. In this paper we con sider the modulated versions of the 1d periodic or non-periodic Korteweg–de Vries (KdV) equatio n and of the modified KdV equation. For that we use a deterministic notion of ”irregularity” fo r the modulation and obtain local and global results similar to those valid without modulation. In so me cases the irregularity of the modulation improves the well-posedness theory of the equat ions. Our approach is based on estimates for the regularising effect of the modulated dispersion on the non-linear term using the theory of controlled paths and estimates stemming from Young’s th eory of integration.

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