Cubic NLW/NLKG on R2
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- Scaling is sc = 0.
- 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.
- For
- Remark: This is a symplectic flow with the symplectic form of H1 / 2, as in the one-dimensional case.
