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|Type:||Artigo de periódico|
|Title:||On The Cauchy Problem For A Coupled System Of Kdv Equations: Critical Case|
|Abstract:||We investigate some well-posedness issues for the initial value problem associated to the system for given data in low order Sobolev spaces Hs(R) × Hs(R). We prove local and global well-posedness results utilizing the sharp smoothing es-timates associated to the linear problem combined with the contraction mapping principle. For data with small Sobolev norm we obtain global solution whenever s ≥ 0 by using global smoothing estimates. In particular, for data satisfying where S is solitary wave solution, we get global solution whenever s > 3/4. To prove this last result, we apply the splitting argument introduced by Bourgain  and further simplied by Fonseca, Linares and Ponce [6,7].|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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