Cubic NLS on S6: Difference between revisions

Revision as of 20:12, 9 August 2006

The theory of the cubic NLS on the six-dimensional sphere is as follows.

Scaling is $s_{c}=2\,$ .
Uniform LWP holds in $H^{s}\,$ for $s>5/2\,$ BuGdTz-p3.
Uniform LWP fails in the energy class $H^{1}\,$ BuGdTz2002; indeed we have this failure for any NLS on $S^{6}$ , even ones for which the energy is subcritical. This is in contrast to the Euclidean case, where one has LWP for powers $p<2\,$ .

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 * 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 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:Schrodinger]]