Quotients of Navier--Stokes equation on space curves

TL;DR

This paper investigates a Navier--Stokes system on a space curve, deriving a quotient equation to find solutions and reducing it to ODE systems using virial expansion of the Planck potential.

Contribution

It introduces a quotient equation for Navier--Stokes on curves and applies virial expansion to simplify solution finding.

Findings

Derived quotient equation for Navier--Stokes on curves

Reduced quotient equation to ODE systems using virial expansion

Found some solutions of the Navier--Stokes system

Abstract

A Navier--Stokes system on a curve is discussed. The quotient equation for this system is found. The quotient is used to find some solutions of Navier--Stokes system. Using virial expansion of the Planck potential, we reduce the quotient equation to a series of systems of ordinary differential equations.