Statistical conservation laws for scalar model problems: Hierarchical evolution equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909746858033152 |
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| author | Huang, Qian Rohde, Christian |
| author_facet | Huang, Qian Rohde, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15359 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical conservation laws for scalar model problems: Hierarchical evolution equations Huang, Qian Rohde, Christian Analysis of PDEs Numerical Analysis 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. |
| title | Statistical conservation laws for scalar model problems: Hierarchical evolution equations |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2508.15359 |