On the existence time of local solutions for critical semilinear Schrödinger equations in Sobolev spaces

Tsukasa Iwabuchi; Makoto Nakamura

doi:10.1016/j.nonrwa.2016.06.009

On the existence time of local solutions for critical semilinear Schrödinger equations in Sobolev spaces

Tsukasa Iwabuchi, Makoto Nakamura

SCI - Mathematics

Yamagata University

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

Abstract

The existence time of local solutions of semilinear Schrödinger equations in Sobolev spaces is considered based on the method of frequency decomposition. The semilinear terms are power type or exponential type, which are critical in terms of the scaling or the Trudinger–Moser inequality. The existence time is estimated by the low and high frequency parts of data.

Original language	English
Pages (from-to)	168-180
Number of pages	13
Journal	Nonlinear Analysis: Real World Applications
Volume	33
DOIs	https://doi.org/10.1016/j.nonrwa.2016.06.009
Publication status	Published - 2017 Feb 1

Keywords

Cauchy problem
Local solution
Semilinear Schrödinger equation

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10.1016/j.nonrwa.2016.06.009

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title = "On the existence time of local solutions for critical semilinear Schr{\"o}dinger equations in Sobolev spaces",

abstract = "The existence time of local solutions of semilinear Schr{\"o}dinger equations in Sobolev spaces is considered based on the method of frequency decomposition. The semilinear terms are power type or exponential type, which are critical in terms of the scaling or the Trudinger–Moser inequality. The existence time is estimated by the low and high frequency parts of data.",

keywords = "Cauchy problem, Local solution, Semilinear Schr{\"o}dinger equation",

author = "Tsukasa Iwabuchi and Makoto Nakamura",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Ltd",

year = "2017",

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AU - Nakamura, Makoto

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N2 - The existence time of local solutions of semilinear Schrödinger equations in Sobolev spaces is considered based on the method of frequency decomposition. The semilinear terms are power type or exponential type, which are critical in terms of the scaling or the Trudinger–Moser inequality. The existence time is estimated by the low and high frequency parts of data.

AB - The existence time of local solutions of semilinear Schrödinger equations in Sobolev spaces is considered based on the method of frequency decomposition. The semilinear terms are power type or exponential type, which are critical in terms of the scaling or the Trudinger–Moser inequality. The existence time is estimated by the low and high frequency parts of data.

KW - Cauchy problem

KW - Local solution

KW - Semilinear Schrödinger equation

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JF - Nonlinear Analysis: Real World Applications

ER -

On the existence time of local solutions for critical semilinear Schrödinger equations in Sobolev spaces

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Keywords

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