Endpoint Strichartz estimates with angular integrability and some applications

Jungkwon Kim; Yoonjung Lee; Ihyeok Seo

doi:10.1007/s00028-022-00797-4

Endpoint Strichartz estimates with angular integrability and some applications

Jungkwon Kim
, Yoonjung Lee
, Ihyeok Seo

Department of Mathematics

Sungkyunkwan University

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

Abstract

The endpoint Strichartz estimate ‖eitΔf‖Lt2Lx∞≲‖f‖L2 is known to be false in two space dimensions. Taking averages spherically on the polar coordinates x= ρω, ρ> 0 , ω∈ S¹, Tao showed a substitute of the form ‖eitΔf‖Lt2Lρ∞Lω2≲‖f‖L2. Here we address a weighted version of such spherically averaged estimates. As an application, the existence of solutions for the inhomogeneous nonlinear Schrödinger equation is shown for L² data.

Original language	English
Article number	37
Journal	Journal of Evolution Equations
Volume	22
Issue number	2
DOIs	https://doi.org/10.1007/s00028-022-00797-4
State	Published - Jun 2022

Keywords

Nonlinear Schrödinger equations
Weighted estimates
Well-posedness

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10.1007/s00028-022-00797-4

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title = "Endpoint Strichartz estimates with angular integrability and some applications",

abstract = "The endpoint Strichartz estimate ‖eitΔf‖Lt2Lx∞≲‖f‖L2 is known to be false in two space dimensions. Taking averages spherically on the polar coordinates x= ρω, ρ> 0 , ω∈ S1, Tao showed a substitute of the form ‖eitΔf‖Lt2Lρ∞Lω2≲‖f‖L2. Here we address a weighted version of such spherically averaged estimates. As an application, the existence of solutions for the inhomogeneous nonlinear Schr{\"o}dinger equation is shown for L2 data.",

keywords = "Nonlinear Schr{\"o}dinger equations, Weighted estimates, Well-posedness",

author = "Jungkwon Kim and Yoonjung Lee and Ihyeok Seo",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = jun,

doi = "10.1007/s00028-022-00797-4",

language = "English",

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T1 - Endpoint Strichartz estimates with angular integrability and some applications

AU - Kim, Jungkwon

AU - Lee, Yoonjung

AU - Seo, Ihyeok

PY - 2022/6

Y1 - 2022/6

N2 - The endpoint Strichartz estimate ‖eitΔf‖Lt2Lx∞≲‖f‖L2 is known to be false in two space dimensions. Taking averages spherically on the polar coordinates x= ρω, ρ> 0 , ω∈ S1, Tao showed a substitute of the form ‖eitΔf‖Lt2Lρ∞Lω2≲‖f‖L2. Here we address a weighted version of such spherically averaged estimates. As an application, the existence of solutions for the inhomogeneous nonlinear Schrödinger equation is shown for L2 data.

AB - The endpoint Strichartz estimate ‖eitΔf‖Lt2Lx∞≲‖f‖L2 is known to be false in two space dimensions. Taking averages spherically on the polar coordinates x= ρω, ρ> 0 , ω∈ S1, Tao showed a substitute of the form ‖eitΔf‖Lt2Lρ∞Lω2≲‖f‖L2. Here we address a weighted version of such spherically averaged estimates. As an application, the existence of solutions for the inhomogeneous nonlinear Schrödinger equation is shown for L2 data.

KW - Nonlinear Schrödinger equations

KW - Weighted estimates

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/85128331388

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DO - 10.1007/s00028-022-00797-4

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SN - 1424-3199

VL - 22

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

IS - 2

M1 - 37

ER -

Endpoint Strichartz estimates with angular integrability and some applications

Abstract

Keywords

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