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<p>Singularities in the network flow are modeled by self-similarly shrinking solutions known as regular shrinkers. In this work, we investigate whether regular shrinkers are stable. We show that all regular shrinkers enclosing two or more regions are unstable under perturbations. Among those enclosing a single region, the 4-ray star, 5-ray star, fish, and rocket shrinkers are also shown to be unstable.</p>

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Stability of Regular Shrinkers in the Network Flow

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Jui-En Chang

摘要

Singularities in the network flow are modeled by self-similarly shrinking solutions known as regular shrinkers. In this work, we investigate whether regular shrinkers are stable. We show that all regular shrinkers enclosing two or more regions are unstable under perturbations. Among those enclosing a single region, the 4-ray star, 5-ray star, fish, and rocket shrinkers are also shown to be unstable.