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Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2012

Rough solutions for the periodic Korteweg-de Vries equation

Résumé

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 $\FF L^{\alpha,p}$ spaces. We discuss convergence of Galerkin approximations, a modified Euler scheme and the presence of a random force of white-noise type in time.

Dates et versions

hal-00858789 , version 1 (06-09-2013)

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Massimiliano Gubinelli. Rough solutions for the periodic Korteweg-de Vries equation. Communications on Pure and Applied Mathematics, 2012, 11 (2), pp.709 - 733. ⟨10.3934/cpaa.2012.11.709⟩. ⟨hal-00858789⟩
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