Quintic NLS on R3: Difference between revisions

Revision as of 23:00, 15 September 2006

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

Scaling is $s_{c}=1\,$ .
LWP is known for $s\geq 1\,$ $s\geq 1\,$ 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 $s\geq 1\,$ $s\geq 1\,$ in the defocusing case CoKeStTkTa-p
- For radial data this is in Bo1999b, Bo1999.
- Blowup can occur in the focussing case from Glassey's virial identity.

@@ Line 6: / Line 6: @@
 ** For <math>s<s_c\,</math> we have ill-posedness, indeed the <math>H^s\,</math> 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 <math>s\ge 1\,</math> in the defocusing case [[CoKeStTkTa-p]]
-** For radial data this is in [[Bo-p]], [[Bo1999]].
+** For radial data this is in [[Bo1999b]], [[Bo1999]].
 ** Blowup can occur in the focussing case from Glassey's virial identity.
 [[Category:Schrodinger]]
 [[Category:Equations]]