On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications

Chu-Hee  Cho; Youngwoo  Koh; Ihyeok  Seo

doi:10.3934/dcds.2016.36.1905

Article Contents

2016, Volume 36, Issue 4: 1905-1926. Doi: 10.3934/dcds.2016.36.1905

This issue Previous Article Boundary blow-up solutions to fractional elliptic equations in a measure framework Next Article Global solutions to a one-dimensional non-conservative two-phase model

On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications

1.
Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784
2.
School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722
3.
Department of Mathematics, Sungkyunkwan University, Suwon 440-746

Received: December 31, 2014

Revised: June 30, 2015

Published: May 2017

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Abstract

In this paper we obtain some new inhomogeneous Strichartz estimates for the fractional Schrödinger equation in the radial case. Then we apply them to the well-posedness theory for the equation $i\partial_{t}u+|\nabla|^{\alpha}u=V(x,t)u$, $1<\alpha<2$, with radial $\dot{H}^\gamma$ initial data below $L^2$ and radial potentials $V\in L_t^rL_x^w$ under the scaling-critical range $\alpha/r+n/w=\alpha$.

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Mathematics Subject Classification: Primary: 35B45, 35A01; Secondary: 35Q40.

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