On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data

Ryosuke Hyakuna; Masayoshi Tsutsumi

doi:10.1090/S0002-9939-2012-11314-0

On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} ^p-initial data

Ryosuke Hyakuna, Masayoshi Tsutsumi

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

12 Citations (Scopus)

Abstract

We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u ₀ ∈ L{frown} ^p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.

Original language	English
Pages (from-to)	3905-3920
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2012-11314-0
Publication status	Published - 2012

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9939-2012-11314-0

Fingerprint Dive into the research topics of 'On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} <sup>p</sup>-initial data'. Together they form a unique fingerprint.

Cite this

@article{11fcc32ea03745d1ab7c06e1d87005c2,

title = "On existence of global solutions of schr{\"o}dinger equations with subcritical nonlinearity for L{frown} p-initial data",

abstract = "We construct a local theory of the Cauchy problem for the nonlinear Schr{\"o}dinger equations with α ∈ (1, 5) and u 0 ∈ L{frown} p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.",

author = "Ryosuke Hyakuna and Masayoshi Tsutsumi",

year = "2012",

doi = "10.1090/S0002-9939-2012-11314-0",

language = "English",

volume = "140",

pages = "3905--3920",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "11",

}

TY - JOUR

T1 - On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data

AU - Hyakuna, Ryosuke

AU - Tsutsumi, Masayoshi

PY - 2012

Y1 - 2012

N2 - We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u 0 ∈ L{frown} p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.

AB - We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u 0 ∈ L{frown} p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.

UR - http://www.scopus.com/inward/record.url?scp=84863936063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863936063&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2012-11314-0

DO - 10.1090/S0002-9939-2012-11314-0

M3 - Article

AN - SCOPUS:84863936063

VL - 140

SP - 3905

EP - 3920

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11