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arXiv · 2501.16455

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

Olga S. Rozanova·Marko K. Turzynsky
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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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Olga S. Rozanova, Marko K. Turzynsky. 2025-01-27. Linearization method and sharp thresholds for spherically symmetric multidimensional pressureless Euler-Poisson equations. https://arxiv.org/abs/2501.16455

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