Differential and Integral Equations

Critical well-posedness and scattering results for fractional Hartree-type equations

Sebastian Herr and Changhun Yang

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Abstract

Scattering for the mass-critical fractional Schrödinger equation with a cubic Hartree-type nonlinearity for initial data in a small ball in the scale-invariant space of three-dimensional radial and square-integrable initial data is established. For this, we prove a bilinear estimate for free solutions and extend it to perturbations of bounded quadratic variation. This result is shown to be sharp by proving the discontinuity of the flow map in the super-critical range.

Article information

Source
Differential Integral Equations, Volume 31, Number 9/10 (2018), 701-714.

Dates
First available in Project Euclid: 13 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1528855436

Mathematical Reviews number (MathSciNet)
MR3814563

Zentralblatt MATH identifier
06945778

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35Q40: PDEs in connection with quantum mechanics

Citation

Herr, Sebastian; Yang, Changhun. Critical well-posedness and scattering results for fractional Hartree-type equations. Differential Integral Equations 31 (2018), no. 9/10, 701--714. https://projecteuclid.org/euclid.die/1528855436


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