Scattering for a class of non-radial inhomogeneous bi-harmonic Hartree equations

TL;DR

This paper establishes energy scattering for global solutions of a non-radial, inhomogeneous bi-harmonic Hartree equation in the inter-critical regime, extending previous results by removing symmetry assumptions using a novel approach.

Contribution

It introduces a new method to prove energy scattering for non-radial solutions of a fourth-order Hartree equation, removing the need for symmetry assumptions.

Findings

Proves energy scattering for non-radial solutions

Extends previous radial symmetry results

Uses a new approach based on Dodson-Murphy techniques

Abstract

This manuscript proves the energy scattering of global solutions to a repulsive fourth-order generalized Hartree equation with non-radial data in the inter-critical regime. This work uses a new approach due to Dodson-Murphy [4] and extends the previous work [14] by removing the spherically symmetric assumption on the data.