Rough solutions for the periodic Korteweg-de Vries equation

M. Gubinelli

First issued 30 September 2006 · PDF

Abstract

We show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensional Korteweg–de Vries (KdV) equation on a periodic domain and with initial condition in ${\mathcal{F}} L^{\alpha,p}$ spaces. We discuss convergence of Galerkin approximations, a modified Euler scheme and the presence of a random force of white-noise type in time.

Versions

1. Version 3 (arXiv v3) current
   20 July 2009
   arXiv comments: 24 pages, no figures, major changes and discussion of $FL^{α,p}$ spaces
   PDF · LaTeX source · files and digests · arXiv:math/0610006
2. Version 2 (arXiv v2)
   11 July 2007
   arXiv comments: 28 pages, no figures
   PDF · LaTeX source · files and digests · arXiv:math/0610006
3. Version 1 (arXiv v1)
   30 September 2006
   arXiv comments: 25 pages, no figures
   PDF · LaTeX source · files and digests · arXiv:math/0610006

Cite

M. Gubinelli. Rough solutions for the periodic Korteweg-de Vries equation. Papers of Massimiliano Gubinelli, 2006, version 3. https://mgubi.org/papers/paper/rough-periodic-kdv/

Licence: arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors

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