Critical Thresholds in 2D Restricted Euler-Poisson Equations

2002/03/15 by Hailiang Liu, Eitan Tadmor, Liu, Hailiang +1 · 1 citation
Mathematics · #35B30 #35Q35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP #msc:35B30 #msc:35Q35

paper · pdf · doi:10.48550/arxiv.math/0203145

arxiv created 2002/03/15 · openalex publication_date 2002/03/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a complete description of the critical threshold phenomena for the two-dimensional localized Euler-Poisson equations, introduced by the authors in [Liu & Tadmor, Comm. Math Phys., To appear]. Here, the questions of global regularity vs. finite-time breakdown for the 2D Restricted Euler-Poisson solutions are classified in terms of precise explicit formulae, describing a remarkable variety of critical threshold surfaces of initial configurations. In particular, it is shown that the 2D critical thresholds depend on the relative size of three quantities: the initial density, the initial divergence as well as the initial spectral gap, that is, the difference between the two eigenvalues of the 2 × 2 initial velocity gradient.

Cited by

• Large-time behavior of pressureless Euler--Poisson equations with background states

Related

• Critical Thresholds in Euler-Poisson Equations
• Critical Thresholds in One Dimensional Damped Euler-Poisson Systems
• Critical thresholds in pressureless Euler--Poisson equations with background states
• On the global regularity of sub-critical Euler-Poisson equations with pressure
• A complete characterization of sharp thresholds to spherically symmetric multidimensional pressureless Euler-Poisson systems