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September/October 2018 Critical well-posedness and scattering results for fractional Hartree-type equations
Sebastian Herr, Changhun Yang
Differential Integral Equations 31(9/10): 701-714 (September/October 2018).

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.

Citation

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Sebastian Herr. Changhun Yang. "Critical well-posedness and scattering results for fractional Hartree-type equations." Differential Integral Equations 31 (9/10) 701 - 714, September/October 2018.

Information

Published: September/October 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06945778
MathSciNet: MR3814563

Subjects:
Primary: 35Q40 , 35Q55

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 9/10 • September/October 2018
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