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arXiv · 2205.06179

A class of exact solutions of the Navier-Stokes equations in three and four dimensions

R. K. Michael Thambynayagam
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Abstract

A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary number of dimensions. We then derive spatially periodic solutions for the velocity and pressure fields that span an unbounded domain in three and four dimensions, given a smooth solenoidal initial velocity vector field. In these solutions all velocity components depend non-trivially on all coordinate directions.

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R. K. Michael Thambynayagam. 2022-05-01. A class of exact solutions of the Navier-Stokes equations in three and four dimensions. https://doi.org/10.1016/j.euromechflu.2023.02.008

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