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 -