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Rough solutions for the periodic Korteweg-de Vries equation

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

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M. Gubinelli. 2009-07-20. Rough solutions for the periodic Korteweg-de Vries equation. https://arxiv.org/abs/math/0610006

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