Septic NLW/NLKG on R: Difference between revisions
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* Scaling is <math>s_c = 1/6</math>. | * Scaling is <math>s_c = 1/6</math>. | ||
* LWP for <math>s \geq 5/14</math> by energy estimates and Sobolev (solution is in <math>L^7_x</math>) | * LWP for <math>s \geq 5/14</math> by energy estimates and Sobolev (solution is in <math>L^7_x</math>) | ||
** For <math>s < 5/14</math> it is not even possible to make sense of the solution as a distribution (note there are no smoothing effects for the 1D wave equation!) and so there is ill-posedness [CtCoTa-p2]. | ** For <math>s < 5/14</math> it is not even possible to make sense of the solution as a distribution (note there are no smoothing effects for the 1D wave equation!) and so there is ill-posedness [[CtCoTa-p2]]. | ||
* GWP for <math>s = 1</math> in the defocusing case by energy conservation. Presumably this is improvable. | * GWP for <math>s = 1</math> in the defocusing case by energy conservation. Presumably this is improvable. | ||
[[Category:Wave]] | [[Category:Wave]] | ||
[[Category:Equations]] | [[Category:Equations]] | ||
Latest revision as of 00:07, 3 February 2007
- Scaling is .
- LWP for by energy estimates and Sobolev (solution is in )
- For it is not even possible to make sense of the solution as a distribution (note there are no smoothing effects for the 1D wave equation!) and so there is ill-posedness CtCoTa-p2.
- GWP for in the defocusing case by energy conservation. Presumably this is improvable.
