Cubic NLW/NLKG on R2

• Scaling is $s_{c}=0$.
• LWP for $s\geq 1/4$ 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 $s\geq 1/2$ for defocussing NLKG Bo1999 and for defocussing NLW [Fo-p]
  • For $s\geq 1$ 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 <math>H^{1/2}</math>, as in [#nlw-3_on_R the one-dimensional case].

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