On the existence of helical invariant solutions to steady Navier-Stokes equations

TL;DR

This paper proves the existence of at least one helical invariant solution to the steady Navier-Stokes equations in a helically symmetric domain under certain boundary conditions and data invariance.

Contribution

It establishes the existence of helical invariant solutions for the steady Navier-Stokes equations with helical symmetric data and boundary conditions.

Findings

Existence of at least one helical invariant solution

Solution exists under compatibility conditions

Applicable to nonhomogeneous boundary value problems

Abstract

In this paper, we investigate the nonhomogeneous boundary value problem for the steady Navier-Stokes equations in a helically symmetric spatial domain. When data is assumed to be helical invariant and satisfies the compatibility condition, we prove this problem has at least one helical invariant solution.