Septic NLW/NLKG on R2

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  • Scaling is sc = 2 / 3.
  • LWP for s \geq s_c by Strichartz estimates (LbSo1995)
    • For s < sc one has instantaneous blowup in the focusing case, and unbounded growth of Hs 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.