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arXiv · 2508.15359

Statistical conservation laws for scalar model problems: Hierarchical evolution equations

Qian Huang·Christian Rohde
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Abstract

The probability density functions (PDFs) for the solution of the incompressible Navier-Stokes equation can be represented by a hierarchy of linear equations. This article develops new hierarchical evolution equations for PDFs of a scalar conservation law with random initial data as a model problem. Two frameworks are developed, including multi-point PDFs and single-point higher-order derivative PDFs. These hierarchies capture statistical correlations and guide closure strategies.

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Qian Huang, Christian Rohde. 2025-08-21. Statistical conservation laws for scalar model problems: Hierarchical evolution equations. https://arxiv.org/abs/2508.15359

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