Year: 2026
Type: preprint
Abstract: The paper concerns the orbital stability of positive standing waves for the logarithmic Choquard equation with a small local nonlinear perturbation. First, the uniqueness and nondegeneracy of the positive ground-state solution are established via bifurcation and compactness arguments. Then, by exploiting the spectral properties of the linearized operator around the positive ground-state solution in high-energy spaces, the orbital stability of the corresponding positive standing wave is proved. The main difficulty in establishing orbital stability stems from the fact that the logarithmic convolution kernel is both sign-changing and strongly singular, while the norm used to prove global existence is not translation invariant. Consequently, existing approaches to orbital stability for positive ground-state solutions of three-and higher-dimensional Choquard equations with Riesz-type kernels cannot be applied to the two-dimensional logarithmic Choquard equation considered here.
Source: arXiv (Cornell University)
Authors: Liu, Zhisu, Sun, Shu-Ming, Zhang, Weinian
Institutions: Sichuan University, Virginia Tech
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223876978