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arXiv · 2308.14194

Generalized equations of hydrodynamics in fractional derivatives

P. Kostrobij·B. Markovych·I. Ryzha·M. Tokarchuk
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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 ($\beta=1/k_{B}T =const$), 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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P. Kostrobij, B. Markovych, I. Ryzha, M. Tokarchuk. 2023-08-27. Generalized equations of hydrodynamics in fractional derivatives. https://arxiv.org/abs/2308.14194

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