A bilinear fractional integral operator for Euler–Riesz systems
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.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Differential Equations and Boundary Problems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Analysis & PDE
- Volume
- 19
- Issue
- 4
- Pages
- 823–846
- Publication date
- 17 May 2026
- Language
- EN