کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8896567 1630585 2014 51 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Global in time Strichartz estimates for the fractional Schrödinger equations on asymptotically Euclidean manifolds
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Global in time Strichartz estimates for the fractional Schrödinger equations on asymptotically Euclidean manifolds
چکیده انگلیسی
In this paper, we prove global in time Strichartz estimates for the fractional Schrödinger operators, namely e−itΛgσ with σ∈(0,∞)\{1} and Λg:=−Δg where Δg is the Laplace-Beltrami operator on asymptotically Euclidean manifolds (Rd,g). Let f0∈C0∞(R) be a smooth cutoff equal 1 near zero. We firstly show that the high frequency part (1−f0)(P)e−itΛgσ satisfies global in time Strichartz estimates as on Rd of dimension d≥2 inside a compact set under non-trapping condition. On the other hand, under the moderate trapping assumption (1.12), the high frequency part also satisfies the global in time Strichartz estimates outside a compact set. We next prove that the low frequency part f0(P)e−itΛgσ satisfies global in time Strichartz estimates as on Rd of dimension d≥3 without using any geometric assumption on g. As a byproduct, we prove global in time Strichartz estimates for the fractional Schrödinger and wave equations on (Rd,g), d≥3 under non-trapping condition.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 275, Issue 8, 15 October 2018, Pages 1943-2014
نویسندگان
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