Artículos de revistas
THE SUPERCRITICAL GENERALIZED KDV EQUATION: GLOBAL WELL-POSEDNESS IN THE ENERGY SPACE AND BELOW
Registro en:
Mathematical Research Letters. Int Press Boston, Inc, v. 18, n. 2, n. 357, n. 377, 2011.
1073-2780
WOS:000289375500013
Autor
Farah, LG
Linares, F
Pastor, A
Institución
Resumen
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) 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. 18 2 357 377 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)