# The Korteweg-de Vries equation on the half-line with smooth and rough data

HY2W02 - Analysis of dispersive systems

The well-posedness of the initial-boundary value problem (ibvp) for the Korteweg-de Vries equation  on the half-line  is studied for initial data  in spatial Sobolev spaces $H^{s}(0, \infty)$, $s>-3/4$, and boundary data in  thetemporal Sobolev spaces suggested by the time regularity of the Cauchy problem for the corresponding linear equation. First, linear estimates in Hadamard and Bourgain spaces are derived by utilizing the Fokas solution formula of the ibvp for the forced linear equation. Then, using these and  the needed bilinear estimates, it is shown that the iteration map defined by the Fokas solution formula is a contraction in an appropriate solution space. This is based on work in collaboration with Athanassios Fokas, Dionyssis Mantzavinos and Fangchi Yan.

This talk is part of the Isaac Newton Institute Seminar Series series.