Quintic NLW/NLKG on R2
- Scaling is sc = 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 < sc one has instantaneous blowup in the focusing case, and unbounded growth of Hs norms in the defocusing case (CtCoTa-p2)
- GWP for s > 3 / 4 for defocussing NLW/NLKG (Fo-p)
- For this follows energy conservation.
- One also has GWP and scattering for data with small H1 / 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.