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

On inhomogeneous strichartz estimates for fractional Schrödinger equations and their applications

Chu Hee Cho
, Youngwoo Koh
, Ihyeok Seo

Department of Mathematics

Pohang University of Science and Technology
Korea Institute for Advanced Study

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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∂_tu + |∇|^αu = V (x, t)u, 1 < α < 2, with radial H^γ initial data below L² and radial potentials V ∈ L^r_t L^w_x under the scaling-critical range α/r + n/w = α.

Original language	English
Pages (from-to)	1905-1926
Number of pages	22
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2016.36.1905
State	Published - 1 Apr 2016

Keywords

Schrödinger equations
Strichartz estimates
Well-posedness

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title = "On inhomogeneous strichartz estimates for fractional Schr{\"o}dinger equations and their applications",

abstract = "In this paper we obtain some new inhomogeneous Strichartz estimates for the fractional Schr{\"o}dinger equation in the radial case. Then we apply them to the well-posedness theory for the equation i∂tu + |∇|αu = V (x, t)u, 1 < α < 2, with radial Hγ initial data below L2 and radial potentials V ∈ Lrt Lwx under the scaling-critical range α/r + n/w = α.",

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author = "Cho, \{Chu Hee\} and Youngwoo Koh and Ihyeok Seo",

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AU - Cho, Chu Hee

AU - Koh, Youngwoo

AU - Seo, Ihyeok

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Y1 - 2016/4/1

N2 - 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∂tu + |∇|αu = V (x, t)u, 1 < α < 2, with radial Hγ initial data below L2 and radial potentials V ∈ Lrt Lwx under the scaling-critical range α/r + n/w = α.

AB - 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∂tu + |∇|αu = V (x, t)u, 1 < α < 2, with radial Hγ initial data below L2 and radial potentials V ∈ Lrt Lwx under the scaling-critical range α/r + n/w = α.

KW - Schrödinger equations

KW - Strichartz estimates

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/84943563313

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DO - 10.3934/dcds.2016.36.1905

M3 - Article

AN - SCOPUS:84943563313

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SP - 1905

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

ER -

On inhomogeneous strichartz estimates for fractional Schrödinger equations and their applications

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Keywords

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