Difference between revisions of "Bilinear Airy estimates"

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* The <math>-3/4+</math> estimate [[references.html#KnPoVe1996 KnPoVe1996]] on '''R'''<nowiki>:</nowiki>
 
* The <math>-3/4+</math> estimate [[references.html#KnPoVe1996 KnPoVe1996]] on '''R'''<nowiki>:</nowiki>
  
<center><math>\| u\partial_x v ||_{X^{-3/4+, -1/2+}} \lesssim \| u \|_{X^{{-3/4+, 1/2+}} \| v \|_{X^{{-3/4+, 1/2+}}</math></center>
+
<center><math>\| u \partial_x v \|_{X^{-3/4+, -1/2+}} \lesssim \| u \|_{X^{-3/4+, 1/2+}} \| v \|_{X^{-3/4+, 1/2+}}</math></center>
  
  

Revision as of 15:12, 28 July 2006

Algebraic identity

Much of the bilinear estimate theory for Airy equation rests on the following "three-wave resonance identity":

whenever

Estimates

The following bilinear estimates are known:


  • Remark: In principle, a complete list of bilinear estimates could be obtained from [[references.html#Ta-p2 Ta-p2]].