Quintic NLW/NLKG on R
- 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.