Cubic NLS on S6: Difference between revisions

From DispersiveWiki
Jump to navigationJump to search
No edit summary
 
mNo edit summary
 
(2 intermediate revisions by 2 users not shown)
Line 3: Line 3:
* 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> [[BuGdTz-p2]]; 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>.
* 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 .