Bilinear Airy estimates

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Revision as of 15:11, 28 July 2006 by Colliand (talk | contribs) (Estimates)

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:

Failed to parse (syntax error): {\displaystyle \| u\partial_x v ||_{X^{-3/4+, -1/2+}} \lesssim \| u \|_{X^{{-3/4+, 1/2+}} \| v \|_{X^{{-3/4+, 1/2+}}}


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