# Cubic NLW/NLKG on R2

• Scaling is ${\displaystyle s_{c}=0}$.
• LWP for ${\displaystyle s\geq 1/4}$ by Strichartz estimates (see e.g. LbSo1995)
• This is sharp by concentration examples in the focusing case; the defocusing case is still open.
• GWP for ${\displaystyle s\geq 1/2}$ for defocussing NLKG Bo1999 and for defocussing NLW Fo-p
• For ${\displaystyle s\geq 1}$ this is clear from energy conservation (for both NLKG and NLW).
• In the focussing case there is blowup from large data by the ODE method.
• Remark: This is a symplectic flow with the symplectic form of ${\displaystyle H^{1/2}}$, as in the one-dimensional case.