Quintic NLW/NLKG on R2

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  • Scaling is .
  • LWP for by Strichartz estimates (see e.g. LbSo1995; earlier references exist)
    • When the time of existence depends on the profile of the data and not just on the norm.
    • For one has instantaneous blowup in the focusing case, and unbounded growth of norms in the defocusing case (CtCoTa-p2)
  • GWP for for defocussing NLW/NLKG (Fo-p)
    • For this follows energy conservation.
    • One also has GWP and scattering for data with small norm for general quintic non-linearities (and for either NLW or NLKG).
    • In the focussing case there is blowup from large data by the ODE method.