2025/08/21 by Qian Huang, Huang, Qian, Christian Rohde +1 · 1 citation
Decision Sciences · Earth and Planetary Sciences · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2508.15359
openalex publication_date 2025/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.