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|Type:||Artigo de periódico|
|Title:||On well-posedness and wave operator for the gKdV equation|
|Abstract:||We consider the generalized Korteweg-de Vries (gKdV) equation partial derivative(t)u + partial derivative(3)(x)u + mu partial derivative(x)(u(k+1)) = 0, where k > 4 is an integer number and mu = +/- 1. We give an alternative proof of the Kenig, Ponce and Vega result in Kenig, Ponce and Vega (1993) , which asserts local and global well-posedness in (H) over dot(sk) (R), with s(k) = (k similar to 4)/2k. A blow-up alternative in suitable Strichartz-type spaces is also established. The main. tool is a new linear estimate. As a consequence, we also construct a wave operator in the critical space (H) over dot(sk) (R), extending the results of Cote (2006) . (C) 2012 Elsevier Masson SAS. All rights reserved.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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