Quintic NLW/NLKG on R2

Scaling is $s c = 1 / 2$ .
LWP for by Strichartz estimates (see e.g. LbSo1995; earlier references exist)
- When $s = 1 / 2$ the time of existence depends on the profile of the data and not just on the norm.
- For $s < s c$ one has instantaneous blowup in the focusing case, and unbounded growth of $H s$ norms in the defocusing case (CtCoTa-p2)
GWP for s > 3 / 4 for defocussing NLW/NLKG (Fo-p)
- For $s \geq 1$ this follows energy conservation.
- One also has GWP and scattering for data with small $H 1 / 2$ 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.