Annals of Functional Analysis

A note on fourth-order nonlinear Schrödinger equation

Tarek Saanouni

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Abstract

We consider in four space dimensions, the initial value problem for a fourth-order semi-linear Schröodinger equation with exponential type nonlinearity. In the defocusing sign, we obtain unconditional global well-posedness in the energy space. In the focusing case, global well-posedness via existence of ground state holds for small radial data.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 249-266.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1419001464

Digital Object Identifier
doi:10.15352/afa/06-1-19

Mathematical Reviews number (MathSciNet)
MR3297801

Zentralblatt MATH identifier
1316.35268

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Keywords
Fourth-order Schrödinger equation ground state Moser-Trudinger inequality well-posedness

Citation

Saanouni, Tarek. A note on fourth-order nonlinear Schrödinger equation. Ann. Funct. Anal. 6 (2015), no. 1, 249--266. doi:10.15352/afa/06-1-19. https://projecteuclid.org/euclid.afa/1419001464


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