Quintic NLS on R3

From DispersiveWiki

The theory of the quintic NLS on is as follows.

  • Scaling is .
  • LWP is known for CaWe1990.
    • For the time of existence depends on the profile of the data as well as the norm.
    • For we have ill-posedness, indeed the 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.