Quintic NLS on R3

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The theory of the quintic NLS on $\R^3$ is as follows.

Scaling is $s_c = 1\,$ .
LWP is known for CaWe1990.
- For $s=1\,$ the time of existence depends on the profile of the data as well as the norm.
- For $s<s_c\,$ we have ill-posedness, indeed the $H^s\,$ norm can get arbitrarily large arbitrarily quickly CtCoTa-p2. In the focusing case we have instantaneous blowup from the virial identity and scaling.
GWP and scattering for in the defocusing case CoKeStTkTa-p
- For radial data this is in Bo1999b, Bo1999.
- Blowup can occur in the focusing case from Glassey's virial identity.