Septic NLW/NLKG on R2

• Scaling is $s_{c}=2/3$.
• LWP for $s\geq s_{c}$ by Strichartz estimates LbSo1995
  • For $s<s_{c}$ one has instantaneous blowup in the focusing case, and unbounded growth of $H^{s}$ norms in the defocusing case [CtCoTa-p2]
• GWP for $s>6/7$ in the defocusing case [Fo-p]
  • For $s\geq 1$ this follows from energy conservation.

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