The Pressureless Damped Euler-Riesz System in the Critical Regularity Framework

• Published in: Journal of mathematical fluid mechanics Vol. 27; no. 4
• Main Authors: Chi, Meiling, Shou, Ling-Yun, Xu, Jiang
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.11.2025
• Subjects: Cauchy problems; Compressibility; Damping; Darcys law; Density; Eigenvalues; Euler-Lagrange equation; Thermodynamics

We are concerned with a system governing the evolution of the pressureless compressible Euler equations with Riesz interaction and damping in Rd (d≥1), where the interaction force is given by ∇(-Δ)(α-d)/2ρ with d-2<α<d. It is observed by the eigenvalue analysis that the density exhibits fracti...