Morrey's Derivation of Hydrodynamics from Statistical Mechanics: A Modern Exposition
Yuyang Wang
Abstract
This paper is a modern review of C. B. Morrey's 1955 paper on the derivation of the equations of hydrodynamics from statistical mechanics. It has two main parts. First, assuming the existence of certain invariant N -particle phase distributions, Morrey derives formal balance laws for mass, momentum, and energy. Second, he attempts to construct a concrete sequence of such distributions by imposing cell-wise constraints that match the prescribed macroscopic fields (ho, u, e). From this construction, he obtains a Gibbs-type limiting form and finally the Euler equations. Compared to classical results, this regime employs the scaling law of Nε3 = O(1) and leads to a more flexible pressure Peq . Our goal is to explain what Morrey is trying to do, why it's natural and where its most delicate points lie. We will rewrite the argument in a more transparent way, distinguishing carefully between formal derivations, physical input, and statements that still need justification.
Create a lesson
Related papers
Learning Lyapunov Operators for Nonlinear Systems
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández et al.
Existence of Admissible Subsolutions to the Dirichlet Problem for Symmetric Augmented k-Hessian Type Equations in Bounded Domains
Quang Hong Dinh, Bang Van Tran, Ngoan Tien Ha et al.
The Regularity datum on time-varying graph domains and Dirichlet--Regularity duality
Martin Dindoš
Existence of flat blowups at boundary points of anisotropic minimizing hypercurrents
Michael Novack, Reinaldo Resende
Isolated singularities of the capillary equation with negative gravity
Bin Deng, Jiahuan Li, Yilu Liu et al.
Local behavior for solutions to inhomogeneous singular parabolic p-Laplace equations
Xia Hao, Yan Li, Zhiwen Zhao