- Scaling is .
- For LWP is known for by Strichartz estimates. This is sharp by scaling argumentsin both the focusing and defocusing cases CtCoTa-p2
- For LWP is known for by Strichartz estimates. This is sharp by concentration arguments in the focusing case; the defocusing case is open.
- In the defocusing case one has GWP for Fo-p
- For one has LWP for by energy estimates and Sobolev (solution is in ). Below this regularity one cannot even make sense of the solution as a distribution.