Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with Large Initial Data of Spherical Symmetry

报告题目：Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with Large Initial Data of Spherical Symmetry

报 告 人： 袁迪凡 博士，北京师范大学

报告时间：2025年 8月27日上午 10：00-11：00

报告地点：思源楼615

报告摘要：The compressible Euler-Riesz equations are fundamental with wide applications in astrophysics, plasma physics, and mathematical biology. In this talk, I will talk about the global existence and nonlinear stability of finite-energy solutions of the multidimensional Euler-Riesz equations with large initial data of spherical symmetry. In particular, both attractive and repulsive interactions for a wide range of Riesz and logarithmic potentials for dimensions larger than or equal to two is considered. Furthermore, I will present the nonlinear stability of global finite-energy solutions for the compressible Euler-Riesz equations around steady states by employing concentration compactness arguments. Steady states properties are obtained by variational arguments connecting to recent advances in aggregation-diffusion equations.