Stochastic differential equations for non-linear hydrodynamics

TL;DR

This paper develops stochastic differential equations for non-linear hydrodynamic fluctuations, incorporating non-Gaussian random forces and explicit Wiener process-based expressions, advancing the modeling of complex fluid dynamics.

Contribution

It introduces non-linear stochastic hydrodynamic equations with explicit non-Gaussian random force representations, extending classical linear theories.

Findings

Derived explicit expressions for non-Gaussian random forces

Formulated non-linear stochastic equations for hydrodynamics

Enhanced understanding of fluctuation dynamics in complex fluids

Abstract

We formulate the stochastic differential equations for non-linear hydrodynamic fluctuations. The equations incorporate the random forces through a random stress tensor and random heat flux as in the Landau and Lifshitz theory. However, the equations are non-linear and the random forces are non-Gaussian. We provide explicit expressions for these random quantities in terms of the well-defined increments of the Wienner process.