Four-dimensional equation of motion for viscous compressible and charged fluid with regard to the acceleration field, pressure field and dissipation field

TL;DR

This paper derives a comprehensive four-dimensional equation of motion for viscous, compressible, charged fluids incorporating acceleration, pressure, and dissipation fields, extending classical fluid dynamics with electromagnetic interactions.

Contribution

It introduces a novel four-potential framework for viscous charged fluids, unifying dissipation, electromagnetic, and gravitational effects in a single equation.

Findings

Equation reduces to Navier-Stokes in weak field limit

Provides equations for kinetic energy loss and velocity dependence

Enables solving fluid motion in gravitational and electromagnetic fields

Abstract

From the principle of least action the equation of motion for viscous compressible and charged fluid is derived. The viscosity effect is described by the 4-potential of the energy dissipation field, dissipation tensor and dissipation stress-energy tensor. In the weak field limit it is shown that the obtained equation is equivalent to the Navier-Stokes equation. The equation for the power of the kinetic energy loss is provided, the equation of motion is integrated, and the dependence of the velocity magnitude is determined. A complete set of equations is presented, which suffices to solve the problem of motion of viscous compressible and charged fluid in the gravitational and electromagnetic fields.