Eulerian dynamics in multi-dimensions with radial symmetry

2020/07/30 by Changhui Tan, Tan, Changhui · 2 citations
Engineering · Environmental Science · Mathematics · #35Q35 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Methane Hydrates and Related Phenomena #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2007.15758

openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the global wellposedness of pressure-less Eulerian dynamics in multi-dimensions, with radially symmetric data. Compared with the 1D system, a major difference in multi-dimensional Eulerian dynamics is the presence of the spectral gap, which is difficult to control in general. We propose a new pair of scalar quantities that provides a significant better control of the spectral gap. Two applications are presented. (i) the Euler-Poisson equations: we show a sharp threshold condition on initial data that distinguish global regularity and finite time blowup; (ii) the Euler-alignment equations: we show a large subcritical region of initial data that leads to global smooth solutions.

Cited by

• Sticky particle Cucker-Smale dynamics and the entropic selection principle for the 1D Euler-alignment system
• Critical thresholds in the Euler-Poisson-alignment system

Related

• A complete characterization of sharp thresholds to spherically symmetric multidimensional pressureless Euler-Poisson systems
• Critical threshold for global regularity of Euler-Monge-Ampère system with radial symmetry
• Global Regularity of the 4D Restricted Euler Equations
• Global regularity for a 1D Euler-alignment system with misalignment
• Global regularity for 1D Eulerian dynamics with singular interaction forces