A bilinear Airy- estimate with application to gKdV-3
A Gruenrock
Abstract
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 Hs, s > -1/6. For real valued data in L2 global wellposedness follows by the conservation of the L2-norm. The main new tool is a bilinear estimate for solutions of the Airy- equation.
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