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SUMMARY:Small data global existence for systems of wave equations: The rol
 e of asymptotics - Istvan Kadar (University of Cambridge)
DTSTART:20230207T140000Z
DTEND:20230207T150000Z
UID:TALK197098@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:Systems of wave equations may fail to be globally well-posed\,
  even for small initial data. Attempts to classify systems into well-\, an
 d ill-posed categories work by identifying structural properties of the eq
 uations that can work as indicators of well-posedness. The most famous of 
 these are the null and weak null conditions. As noted by Keir\, related fo
 rmulations may fail to properly capture the effect of undifferentiated ter
 ms in systems of wave equations. We show that this is because null conditi
 ons are only good for categorising behaviour close to null infinity and pr
 opose an alternative condition for semilinear equations that work for undi
 fferentiated non-linearities as well. Furthermore\, we give an example of 
 a system satisfying the weak null condition with global ill-posedness due 
 to undifferentiated terms.
LOCATION:CMS\, MR13
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