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

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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.",

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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.

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