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Rough solutions for the periodic Korteweg--de~Vries equation

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  • 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 $F L^{\alpha,p}$ spaces. We discuss convergence of Galerkin approximations, a modified Euler scheme and the presence of a random force of white-noise type in time.
    Mathematics Subject Classification: Primary: 35Q53; Secondary: 35D99.


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