Statistical conservation laws for scalar model problems: Hierarchical evolution equations
Analysis of PDEs
2025-08-22 v1 Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.2508.15359,
title = {Statistical conservation laws for scalar model problems: Hierarchical evolution equations},
author = {Qian Huang and Christian Rohde},
journal= {arXiv preprint arXiv:2508.15359},
year = {2025}
}