Quintic NLW/NLKG on R: Difference between revisions
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* Scaling is <math>s_c = 0</math>. | * Scaling is <math>s_c = 0</math>. | ||
* LWP for <math>s \geq 3/10</math> by energy estimates and Sobolev (solution is in <math>L^5_x</math>) | * LWP for <math>s \geq 3/10</math> by energy estimates and Sobolev (solution is in <math>L^5_x</math>) | ||
** For <math>s<3/10</math> one has ill-posedness [CtCoTa-p2], indeed it is not even possible to make sense of solutions in the distributional sense. | ** For <math>s<3/10</math> one has ill-posedness [[CtCoTa-p2]], indeed it is not even possible to make sense of solutions in the distributional sense. | ||
* GWP for <math>s \geq 1</math> in the defocussing case from energy conservation. | * GWP for <math>s \geq 1</math> in the defocussing case from energy conservation. | ||
** It is overwhelmingly likely that one can lower this s index. | ** It is overwhelmingly likely that one can lower this s index. | ||
** In the focussing case there is blowup from large data by the ODE method. | ** In the focussing case there is blowup from large data by the [[ODE method]]. | ||
[[Category:Wave]] | |||
[[Category:Equations]] | |||
Latest revision as of 07:09, 2 August 2006
- Scaling is .
- LWP for by energy estimates and Sobolev (solution is in )
- For one has ill-posedness CtCoTa-p2, indeed it is not even possible to make sense of solutions in the distributional sense.
- GWP for in the defocussing case from energy conservation.
- It is overwhelmingly likely that one can lower this s index.
- In the focussing case there is blowup from large data by the ODE method.
