A bilinear Airy- estimate with application to gKdV-3

Details A bilinear Airy- estimate with application to gKdV-3 A bilinear Airy- estimate with application to gKdV-3

2001-08-28

arxiv.org/abs/math/0108184v2

Mathematics

Analysis of PDEs

A misprint in the online abstract was corrected

Scientific paper

The Fourier restriction norm method is used to show local wellposedness for
the Cauchy Problem for the generalized KdV-equation of order three with data in
the usual Sobolev space H^s, s > -1/6. For real valued data in L^2 global
wellposedness follows by the conservation of the L^2-norm. The main new tool is
a bilinear estimate for solutions of the Airy- equation.

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