# Quintic NLW/NLKG on R2

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