Differential and Integral Equations

A sharp lower bound for the lifespan of small solutions to the Schrödinger equation with a subcritical power nonlinearity

Yuji Sagawa, Hideaki Sunagawa, and Shunsuke Yasuda

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Abstract

Let $T_{\varepsilon}$ be the lifespan for the solution to the Schrödinger equation on $\mathbb R^d$ with a power nonlinearity $\lambda |u|^{2\theta/d}u$ ($\lambda \in \mathbb C$, $0< \theta < 1$) and the initial data in the form $\varepsilon \varphi(x)$. We provide a sharp lower bound estimate for $T_{\varepsilon}$ as $\varepsilon \to +0$ which can be written explicitly by $\lambda$, $d$, $\theta$, $\varphi$ and $\varepsilon$. This is an improvement of the previous result by H. Sasaki [Adv. Diff. Eq., 14 (2009), 1021-1039].

Article information

Source
Differential Integral Equations, Volume 31, Number 9/10 (2018), 685-700.

Dates
First available in Project Euclid: 13 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1528855435

Mathematical Reviews number (MathSciNet)
MR3814562

Zentralblatt MATH identifier
06945777

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B40: Asymptotic behavior of solutions

Citation

Sagawa, Yuji; Sunagawa, Hideaki; Yasuda, Shunsuke. A sharp lower bound for the lifespan of small solutions to the Schrödinger equation with a subcritical power nonlinearity. Differential Integral Equations 31 (2018), no. 9/10, 685--700. https://projecteuclid.org/euclid.die/1528855435


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