A bilinear fractional integral operator for Euler-Riesz systems
Analysis of PDEs
2026-05-27 v2
Abstract
We establish a uniform estimate for a bilinear fractional integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. This estimate is crucial in the integrability analysis of a tensor-valued bilinear fractional integral operator associated with Euler-Riesz systems modeling mean-field interactions induced by a singular kernel. The tensorial operator arises from a reformulation of the Euler-Riesz system that yields a gain in integrability for finite energy solutions through compensated integrability. Additionally, for smooth periodic solutions of the reformulated system, we derive a stability result.
Cite
@article{arxiv.2409.18309,
title = {A bilinear fractional integral operator for Euler-Riesz systems},
author = {Nuno J. Alves and Loukas Grafakos and Athanasios E. Tzavaras},
journal= {arXiv preprint arXiv:2409.18309},
year = {2026}
}