Journal of Integral Equations and Applications

Blow-up of solutions for semilinear fractional Schrödinger equations

A.Z. Fino, I. Dannawi, and M. Kirane

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Abstract

We consider the Cauchy problem in $\mathbb {R}^N$, $N \geq 1$, for the semi-linear Schr\"odinger equation with fractional Laplacian. We present the local well-posedness of solutions in $H^{{\alpha }/{2}}(\mathbb {R}^N)$, $0\lt \alpha \lt 2$. We prove a finite-time blow-up result, under suitable conditions on the initial data.

Article information

Source
J. Integral Equations Applications, Volume 30, Number 1 (2018), 67-80.

Dates
First available in Project Euclid: 10 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1523347338

Digital Object Identifier
doi:10.1216/JIE-2018-30-1-67

Mathematical Reviews number (MathSciNet)
MR3784882

Zentralblatt MATH identifier
06873398

Subjects
Primary: 35B44: Blow-up 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Keywords
Schrödinger equations fractional Laplacian blow-up

Citation

Fino, A.Z.; Dannawi, I.; Kirane, M. Blow-up of solutions for semilinear fractional Schrödinger equations. J. Integral Equations Applications 30 (2018), no. 1, 67--80. doi:10.1216/JIE-2018-30-1-67. https://projecteuclid.org/euclid.jiea/1523347338


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