Generalized equations of hydrodynamics in fractional derivatives

2023/08/27 by P. P. Kostrobij, B. M. Markovych, Kostrobij, P. +5
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Fractional Differential Equations Solutions #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2308.14194

openalex publication_date 2023/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a general approach for obtaining the generalized transport equations with fractional derivatives using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev non-equilibrium statistical operator (NSO) method within the Gibbs statistics. We obtain the non-Markov equations of hydrodynamics for the non-equilibrium average values of densities of particle number, momentum and energy of liquid in a spatially heterogeneous medium with a fractal structure. For isothermal processes (β=1/k_BT =const), the non-Markov Navier-Stokes equation in fractional derivatives is obtained. We consider models for the frequency dependence of memory function (viscosity), which lead to the Navier-Stokes equations in fractional derivatives in space and time.

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