# Quintic NLW/NLKG on R2

• Scaling is sc = 1 / 2.
• LWP for $s \geq 1/2$ 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 $s \geq 1$ 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.