Differential and Integral Equations
- Differential Integral Equations
- Volume 31, Number 9/10 (2018), 701-714.
Critical well-posedness and scattering results for fractional Hartree-type equations
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.
Differential Integral Equations, Volume 31, Number 9/10 (2018), 701-714.
First available in Project Euclid: 13 June 2018
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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