# Cubic NLS on S6

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The theory of the cubic NLS on the six-dimensional sphere is as follows.

- Scaling is .
- Uniform LWP holds in for BuGdTz-p3.
- Uniform LWP fails in the energy class BuGdTz2002; indeed we have this failure for any NLS on , even ones for which the energy is subcritical. This is in contrast to the Euclidean case, where one has LWP for powers .