A class of exact solutions of the Navier-Stokes equations in three and four dimensions
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...
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| description | 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. |
| doi_str_mv | 10.48550/arxiv.2205.06179 |
| format | Article |
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| language | eng |
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| source | Freely Accessible Journals; arXiv.org |
| subjects | Fields (mathematics) Fluid dynamics Fluid flow Incompressible flow Incompressible fluids Mathematical analysis Mathematics - General Mathematics Navier-Stokes equations Physics - Fluid Dynamics |
| title | A class of exact solutions of the Navier-Stokes equations in three and four dimensions |
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