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<p>Inspired by the pioneering work of Escobedo and Velazquez [<CitationRef CitationID="CR30">30</CitationRef>, <CitationRef CitationID="CR31">31</CitationRef>], we develop a new framework to prove that solutions of 4-wave kinetic equations, under very general forms of dispersion relations, develop a condensation at the origin in finite time, under weaker conditions on the initial data than the ones considered in [<CitationRef CitationID="CR30">30</CitationRef>, <CitationRef CitationID="CR31">31</CitationRef>]. We also provide some estimates on the non-condensation times of the solutions.</p>

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Condensation and Non-condensation Times for 4-Wave Kinetic Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月16日

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  • Gigliola Staffilani,
  • Minh-Binh Tran

摘要

Inspired by the pioneering work of Escobedo and Velazquez [30, 31], we develop a new framework to prove that solutions of 4-wave kinetic equations, under very general forms of dispersion relations, develop a condensation at the origin in finite time, under weaker conditions on the initial data than the ones considered in [30, 31]. We also provide some estimates on the non-condensation times of the solutions.