Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/72524
Type: Artigo
Title: The supercritical generalized KdV equation: global well-posedness in the energy space and below
Author: Farah, Luiz G.
Linares, Felipe
Pastor, Ademir
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 >= 5 is an integer number and mu = +/- 1. In the focusing case (mu = 1), we show that if the initial data u(0) belongs to H-1(R) and satisfies E(u(0))M-sk(u(0))(1-sk) < E(Q)M-sk(Q)(1-sk), E(u(0)) >= 0, and parallel to partial derivative(x)u(0)parallel to(sk)(L2)parallel to u(0)parallel to(1-sk)(L2) < parallel to partial derivative(x)Q parallel to(sk)(L2)parallel to Q parallel to(1-sk)(L2), where M(u) and E(u) are the mass and energy, then the corresponding solution is global in H-1(R). Here, s(k) - (k-4)/2k and Q is the ground state solution corresponding to the gKdV equation. In the defocusing case (mu = -1), if k is even, we prove that the Cauchy problem is globally well-posed in the Sobolev spaces H-s(R), s > 4(k-1)/5k.
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 >= 5 is an integer number and mu = +/- 1. In the focusing case (mu = 1), we show that if the i
Subject: Equação de Korteweg-de Vries
Espaços de Sobolev
Problema de Cauchy
Country: Estados Unidos
Editor: International Press
Citation: Mathematical Research Letters. Int Press Boston, Inc, v. 18, n. 2, n. 357, n. 377, 2011.
Rights: Fechado
Identifier DOI: 10.4310/mrl.2011.v18.n2.a13
Address: https://dialnet.unirioja.es/servlet/articulo?codigo=3683138
Date Issue: 2011
Appears in Collections:IMECC - Artigos e Outros Documentos

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