Septic NLW/NLKG on R

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  • Scaling is .
  • LWP for by energy estimates and Sobolev (solution is in )
    • For it is not even possible to make sense of the solution as a distribution (note there are no smoothing effects for the 1D wave equation!) and so there is ill-posedness CtCoTa-p2.
  • GWP for in the defocusing case by energy conservation. Presumably this is improvable.