Cubic NLW/NLKG on R2
- Scaling is .
- LWP for by Strichartz estimates (see e.g. LbSo1995)
- This is sharp by concentration examples in the focusing case; the defocusing case is still open.
- GWP for for defocussing NLKG Bo1999 and for defocussing NLW Fo-p
- For this is clear from energy conservation (for both NLKG and NLW).
- In the focussing case there is blowup from large data by the ODE method.
- Remark: This is a symplectic flow with the symplectic form of , as in the one-dimensional case.