Quintic NLW/NLKG on R

From DispersiveWiki
  • Scaling is .
  • LWP for by energy estimates and Sobolev (solution is in )
    • For one has ill-posedness CtCoTa-p2, indeed it is not even possible to make sense of solutions in the distributional sense.
  • GWP for in the defocussing case from energy conservation.
    • It is overwhelmingly likely that one can lower this s index.
    • In the focussing case there is blowup from large data by the ODE method.