1. A bilinear fractional integral operator for Euler-Riesz systems
- Author
-
Alves, Nuno J., Grafakos, Loukas, and Tzavaras, Athanasios E.
- Subjects
Mathematics - Analysis of PDEs ,42B20, 42B37, 35Q35 - 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.
- Published
- 2024