# Cubic NLW/NLKG on R4

• Scaling is ${\displaystyle s_{c}=1}$.
• LWP for ${\displaystyle s\geq 1}$ by Strichartz estimates (see e.g. LbSo1995; earlier references exist)
• When ${\displaystyle s=1}$ the time of existence depends on the profile of the data and not just on the norm.
• One has strong uniqueness in the energy class Pl-p5, FurPlTer2001. This argument extends to other energy-critical and sub-critical powers in dimensions 4 and higher.
• 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 ${\displaystyle s=1}$ in the defocussing case SaSw1994 (see also Gl1990, Gl1992, Sw1988, Sw1992, BaSa1998, BaGd1997).
• In the focussing case there is blowup from large data by the ODE method.