Linearization method and sharp thresholds for spherically symmetric multidimensional pressureless Euler-Poisson equations

2025/01/27 by Olga Rozanova, Rozanova, Olga S., Marko K. Turzynsky +1
Engineering · Mathematics · #35L60 35L67 35Q60 35Q85 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2501.16455

openalex publication_date 2025/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that the question about the criterion of a singularity formation for radially symmetric solutions to the Cauchy problem for a fairly wide class of equations related to the pressureless Euler-Poisson equations can be reduced to the study of solutions to a linear homogeneous ordinary differential equation. In some cases, such a criterion can be obtained in terms of the initial data. In the remaining cases, it is possible to construct a simple numerical procedure, on the basis of which the question about preserving smoothness for any set of initial data can be solved.

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