Cubic NLW/NLKG on R4

From DispersiveWiki

• Scaling is s_c = 1.
• LWP for by Strichartz estimates (see e.g. LbSo1995; earlier references exist)
  • When 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 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 = 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.