Cubic NLS on S6: Difference between revisions
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* Scaling is <math>s_c = 2\,</math>. | * Scaling is <math>s_c = 2\,</math>. | ||
* Uniform LWP holds in <math>H^s\,</math> for <math>s > 5/2\,</math> [[BuGdTz-p3]]. | * Uniform LWP holds in <math>H^s\,</math> for <math>s > 5/2\,</math> [[BuGdTz-p3]]. | ||
* Uniform LWP fails in the energy class <math>H^1\,</math> [[ | * Uniform LWP fails in the energy class <math>H^1\,</math> [[BuGdTz2002]]; indeed we have this failure for any NLS on <math>S^6</math>, even ones for which the energy is subcritical. This is in contrast to the Euclidean case, where one has LWP for powers <math>p < 2\,</math>. | ||
[[Category:Equations]] | [[Category:Equations]] | ||
[[Category:Schrodinger]] | [[Category:Schrodinger]] | ||
Latest revision as of 06:19, 12 June 2007
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 .
