Probabilistic Descriptions of Fluid Flow: A Survey
Gallenmüller D, Wagner R, Wiedemann E (2023)
Publication Type: Journal article
Publication year: 2023
Journal
Book Volume: 25
Article Number: 52
Journal Issue: 3
DOI: 10.1007/s00021-023-00800-z
Abstract
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the compressible or incompressible Navier–Stokes or Euler equations. The standard concept of weak solution (in the sense of distributions) is still a deterministic one, as it gives exact values for the state variables (like velocity or density) for almost every point in time and space. However, observations and mathematical theory alike suggest that this deterministic viewpoint has certain limitations. Thus, there has been an increased recent interest in the mathematical fluids community in probabilistic concepts of solution. Due to the considerable number of such concepts, it has become challenging to navigate the corresponding literature, both classical and recent. We aim here to give a reasonably concise yet fairly detailed overview of probabilistic formulations of fluid equations, which can roughly be split into measure-valued and statistical frameworks. We discuss both approaches and their relationship, as well as the interrelations between various statistical formulations, focusing on the compressible and incompressible Euler equations.
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Germany (DE)How to cite
APA:
Gallenmüller, D., Wagner, R., & Wiedemann, E. (2023). Probabilistic Descriptions of Fluid Flow: A Survey. Journal of Mathematical Fluid Mechanics, 25(3). https://dx.doi.org/10.1007/s00021-023-00800-z
MLA:
Gallenmüller, Dennis, Raphael Wagner, and Emil Wiedemann. "Probabilistic Descriptions of Fluid Flow: A Survey." Journal of Mathematical Fluid Mechanics 25.3 (2023).
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