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

Prof. Difan Yuan
2025-11-20 14:00-15:00
MCM410

Speaker: Prof. Difan Yuan (Beijing Normal University)
Time: 
14:00-15:00  November 20th, 2025 (Thursday)

Place: MCM410

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

Abstract: 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 , we consider both attractive and repulsive interactions for a wide range of Riesz and logarithmic potentials for dimensions larger than or equal to two.  Moreover, we prove that the nonlinear stability of global finite-energy solutions for the Euler-Riesz equations is unconditional under a spherically symmetric perturbation around the steady solutions. Unlike the Coulomb case where the potential can be represented locally, the singularity and regularity of the nonlocal radial Riesz potential near the origin require careful analysis, which is a crucial step. Steady states properties are obtained by variational arguments connecting to recent advances in aggregation-diffusion equations.