Scholarlink

<p>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 system of ordinary differential equations. If this system turns out to be integrable, then 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Linearization Method and Sharp Thresholds for Radially Symmetric Multidimensional Pressureless Euler-Poisson Equations

  • 期刊论文

  • 发表日期：

    2025年7月6日

查看全文
  • Olga S. Rozanova,
  • Marko K. Turzynsky

摘要

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 system of ordinary differential equations. If this system turns out to be integrable, then 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.