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A class of exact solutions of the Navier-Stokes equations in three and four dimensions (2205.06179v4)
Published 1 May 2022 in math.GM and physics.flu-dyn
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.