TY - JOUR

T1 - LOCAL AND GLOBAL WELL-POSEDNESS FOR THE CRITICAL SCHRODINGER-DEBYE SYSTEM

AU - Oliveira, Filipe Serra de

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We establish local well-posedness results for the Initial Value Problem associated to the Schrodinger-Debye system in dimensions N = 2,3 for data in H-s x H-l, with s and l satisfying max{0, s - 1} <= l <= min{2s, s + 1}. In particular, these include the energy space H-1 x L-2. Our results improve the previous ones obtained by B. Bidegaray, and by A. J. Corcho and F. Linares. Moreover, in the critical case (N = 2) and for initial data in H-1 x L-2, we prove that solutions exist for all times, thus providing a negative answer to the open problem mentioned by G. Fibich and G. C. Papanicolau concerning the formation of singularities for these solutions.

AB - We establish local well-posedness results for the Initial Value Problem associated to the Schrodinger-Debye system in dimensions N = 2,3 for data in H-s x H-l, with s and l satisfying max{0, s - 1} <= l <= min{2s, s + 1}. In particular, these include the energy space H-1 x L-2. Our results improve the previous ones obtained by B. Bidegaray, and by A. J. Corcho and F. Linares. Moreover, in the critical case (N = 2) and for initial data in H-1 x L-2, we prove that solutions exist for all times, thus providing a negative answer to the open problem mentioned by G. Fibich and G. C. Papanicolau concerning the formation of singularities for these solutions.

KW - Perturbed nonlinear Schrodinger equation

KW - global well-posedness

KW - Cauchy problem

U2 - 10.1090/S0002-9939-2013-11612-6

DO - 10.1090/S0002-9939-2013-11612-6

M3 - Article

SN - 0002-9939

VL - 141

SP - 3485

EP - 3499

JO - Proceedings Of The American Mathematical Society

JF - Proceedings Of The American Mathematical Society

IS - 10

ER -