کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593027 1335173 2006 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation
چکیده انگلیسی

We establish that the quadratic non-linear Schrödinger equation iut+uxx=u2,iut+uxx=u2,where u:R×R→Cu:R×R→C, is locally well-posed in Hs(R)Hs(R) when s⩾-1s⩾-1 and ill-posed when s<-1s<-1. Previous work in [C. Kenig, G. Ponce, L. Vega, Quadratic forms for the 1-D semilinear Schrödinger equation, Trans. Amer. Math. Soc. 346 (1996) 3323–3353] had established local well-posedness for s>-34. The local well-posedness is achieved by an iteration using a modification of the standard Xs,bXs,b spaces. The ill-posedness uses an abstract and general argument relying on the high-to-low frequency cascade present in the non-linearity, and a computation of the first non-linear iterate.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 233, Issue 1, 1 April 2006, Pages 228–259
نویسندگان
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