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SUMMARY:The Korteweg-de Vries equation on the half-line with smooth and ro
 ugh data - Alex Himonas (University of Notre Dame)
DTSTART:20220908T133000Z
DTEND:20220908T143000Z
UID:TALK177854@talks.cam.ac.uk
DESCRIPTION:The well-posedness of the initial-boundary value problem&nbsp\
 ;(ibvp) for the Korteweg-de Vries equation&nbsp\; on the half-line&nbsp\; 
 is studied for initial data&nbsp\; in spatial Sobolev spaces $H^{s}(0\, \\
 infty)$\, $s>-3/4$\, and&nbsp\;boundary data in&nbsp\; thetemporal Sobolev
  spaces suggested by the time regularity of the Cauchy problem for the cor
 responding linear equation.&nbsp\;First\, linear estimates in Hadamard and
  Bourgain spaces are derived by utilizing the Fokas solution formula of th
 e ibvp for the forced&nbsp\;linear equation. Then\, using these and&nbsp\;
  the needed bilinear estimates\, it is shown that the iteration map define
 d by the Fokas solution formula is a contraction in an appropriate solutio
 n space.&nbsp\;This is based on work in collaboration with Athanassios Fok
 as\, Dionyssis Mantzavinos and Fangchi Yan.
LOCATION:Seminar Room 1\, Newton Institute
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