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A bilinear Airy- estimate with application to gKdV-3

A Gruenrock
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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 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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A Gruenrock. 2001-08-29. A bilinear Airy- estimate with application to gKdV-3. https://arxiv.org/abs/math/0108184

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