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Author Wei, Dongming ♦ Tadmor, Eitan ♦ Bae, Hantaek
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Initial Configuration ♦ Critical Threshold ♦ Smooth Solution ♦ Electrical Charge E0 Satisfies ♦ Global Smooth Solution ♦ Global Regularity Analysis ♦ Am Subject Classification ♦ Radial Velocity R0 ♦ Radial Symmetry ♦ Radial Setup ♦ Axisymmetric Solution ♦ Repulsive Euler-poisson Equation ♦ Spectral Gap ♦ Certain Threshold ♦ Finite Breakdown ♦ Critical Threshold Phenomenon ♦ Main Difficulty ♦ Multi-dimensional Repulsive Euler-poisson Equation ♦ Symmetric Data ♦ Initial Critical Threshold ♦ Global-in-time Smooth Solution ♦ Configuration Space ♦ Global Regularity ♦ Possible Framework ♦ Radial Case ♦ Global Regularity V
Abstract Abstract. We study the global regularity of multi-dimensional repulsive Euler-Poisson equations in the radial setup. We show that the question of global regularity vs. finite breakdown of smooth solutions depends on whether the initial configuration crosses an initial critical threshold in configuration space. Specifically, there exists a global-in-time smooth solution if and only if the initial configuration of density ρ0, radial velocity R0, and electrical charge e0 satisfies R ′ 0 ≥F(ρ0,e0,R0) for a certain threshold F. Similarly, we characterize the critical threshold for global smooth solutions subject to two-dimensional radially symmetric data with swirl. We also discuss a possible framework for global regularity analysis beyond the radial case, which indicates that the main difficulty lies with bounding the spectral gap, λ2(∇u)−λ1(∇u). Key words. Repulsive Euler-Poisson equations, radial symmetry, axisymmetric solutions with or without swirl, critical threshold phenomena. AMS subject classifications. 35L65, 35D05. 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article