在1D汉堡方程中K41理论和流
1Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, Paris, France; Mathematical Institute, RUDN University, Moscow, Russian Federation; and Steklov Institute, Moscow, Russian Federation.
Chaos (Woodbury, N.Y.)
|February 22, 2024
概括
随机的伯格斯方程模拟了水力动力学流,与科尔摩戈罗夫的方程保持一致.
科学领域:
- 流体动力学 流体动力学
- 随机局部微分方程 随机局部微分方程
- 数学物理 数学物理
背景情况:
- 水力动力学流是一种复杂的现象.
- 科尔摩戈罗夫 (K41) 理论为流提供了基本的预测.
- 之前的启发式证明存在于一些流断言中.
研究的目的:
- 审查最近关于随机汉堡方程的结果.
- 为了证明其作为水力动力学流模型的有效性.
- 为了严格证明与K41理论预测的类比.
主要方法:
- 对小粘度的随机汉堡方程的分析.
- 复习过去二十年的数学结果.
- 基于"一维流和随机汉堡方程" (2021) 的研究成果.
主要成果:
- 随机汉堡方程作为流的一个强大的模型.
- 严格的数学证明提供了关键的流预测.
- 结果为K41理论中的概念提供了严格的基础.
结论:
- 随机汉堡方程是理解流的一个有价值的工具.
- 数学的严谨性支持以前的启发式物理洞察力.
- 这项工作将理论物理与对流的严格数学分析相结合.
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