Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896567 | Journal of Functional Analysis | 2014 | 51 Pages |
Abstract
In this paper, we prove global in time Strichartz estimates for the fractional Schrödinger operators, namely eâitÎgÏ with Ïâ(0,â)\{1} and Îg:=âÎg where Îg is the Laplace-Beltrami operator on asymptotically Euclidean manifolds (Rd,g). Let f0âC0â(R) be a smooth cutoff equal 1 near zero. We firstly show that the high frequency part (1âf0)(P)eâitÎgÏ satisfies global in time Strichartz estimates as on Rd of dimension dâ¥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)eâitÎgÏ satisfies global in time Strichartz estimates as on Rd of dimension dâ¥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), dâ¥3 under non-trapping condition.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Van Duong Dinh,