Zakharov system on R^3: Difference between revisions

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* Zakharov systems do not have a true scale invariance, but the critical regularity is (s0,s1) = (0,-1/2).  
The theory for the [[Zakharov system]] on R^3 is as follows.
* LWP for (1/2,0) [GiTsVl1997]  
 
** For (s0,s1) = (1,0) this was proven in [BoCo1996].  
* The Zakharov system does not have a true scale invariance, but the critical regularity is (s0,s1) = (0,-1/2).  
* GWP for small smooth data is in [OzTs1994].
* Local [[well-posedness]] for (1/2,0) ([[GiTsVl1997]])
** For (s0,s1) = (1,0) this was proven in [[BoCo1996]].  
* GWP for small smooth data is in [[OzTs1994]].


[[Category:Equations]]
[[Category:Equations]]

Latest revision as of 04:54, 4 August 2006

The theory for the Zakharov system on R^3 is as follows.

  • The Zakharov system does not have a true scale invariance, but the critical regularity is (s0,s1) = (0,-1/2).
  • Local well-posedness for (1/2,0) (GiTsVl1997)
    • For (s0,s1) = (1,0) this was proven in BoCo1996.
  • GWP for small smooth data is in OzTs1994.