Rough solutions for the periodic Korteweg-de Vries equation
Analysis of PDEs
2009-07-21 v3 Mathematical Physics
math.MP
Probability
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 spaces. We discuss convergence of Galerkin approximations, a modified Euler scheme and the presence of a random force of white-noise type in time.
Cite
@article{arxiv.math/0610006,
title = {Rough solutions for the periodic Korteweg-de Vries equation},
author = {M. Gubinelli},
journal= {arXiv preprint arXiv:math/0610006},
year = {2009}
}
Comments
24 pages, no figures, major changes and discussion of $FL^{\alpha,p}$ spaces