Analytical solution for 3-dimensional, incompressible Navier-Stokes equations

TL;DR

This paper presents an analytical ad hoc solution to the 3D incompressible Navier-Stokes equations with an external force, demonstrating smoothness, integrability, and Gaussian decay of amplitudes across the entire space.

Contribution

It introduces a novel analytical solution method for the 3D incompressible Navier-Stokes equations with external forcing, highlighting solution smoothness and decay properties.

Findings

Solution is smooth and integrable

Amplitudes exhibit Gaussian decay

Applicable to the whole space

Abstract

This paper provides primarily an analytical ad hoc -solution for 3-dimensional, incompressible Navier-Stokes equations with a suitable external force field. The solution turns out to be smooth and integrable on the whole space. There is gaussian decay of amplitudes.