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SUMMARY:Ill-posedness of truncated series models for water waves - Ambrose
 \, D (Drexel University)
DTSTART:20140731T130000Z
DTEND:20140731T140000Z
UID:TALK53572@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Some numerical methods for water waves\, such as the Craig-Sul
 em method\, involve expanding terms in the water wave evolution equations 
 as series\, truncating those series\, and then simulating the resulting eq
 uations. For one such scheme\, we present analytical evidence that the tru
 ncated system is in fact ill-posed\; this involves further reducing the ev
 olution equations to a model for which we can prove ill-posedness. We then
  present numerical evidence that the full truncated system is ill-posed\, 
 showing that arbitrarily small data can lead to arbitrarily fast growth. W
 e present this numerical evidence for multiple levels of truncation. We ar
 e able to prove that by adding a viscosity to the system\, we instead arri
 ve at a well-posed initial value problem.  This is joint work with Jerry B
 ona and David Nicholls.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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