Difference between revisions of "Septic NLW/NLKG on R"

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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].
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** 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.