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27 April 2024
 
  » arxiv » math.AP/0108184

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A bilinear Airy- estimate with application to gKdV-3
A Gruenrock ;
Date 28 Aug 2001
Subject Analysis of PDEs | math.AP
AbstractThe 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.
Source arXiv, math.AP/0108184
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