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

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Abstract

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.
Original languageUnknown
Pages (from-to)3485-3499
JournalProceedings Of The American Mathematical Society
Volume141
Issue number10
DOIs
Publication statusPublished - 1 Jan 2013

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