Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors
An analytical solution to the Navier–Stokes momentum equations for a compressible flow with volume and small shear viscosities as well as external friction is presented while the dynamic viscosity is set to zero. The demonstrated methodology holds in d dimensions. However, in this study, the three-d...
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2021-05-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0050330 |
| Summary: | An analytical solution to the Navier–Stokes momentum equations for a compressible flow with volume and small shear viscosities as well as external friction is presented while the dynamic viscosity is set to zero. The demonstrated methodology holds in d dimensions. However, in this study, the three-dimensional case is considered in detail. The analytical solution blows up at finite times T, which is determined by a cubic relation if the initial flow velocity is not divergence-free. The existence of T is a necessary and sufficient condition for implementing a singularity. Nonetheless, for external friction μe>T−1, all analytical expressions are smooth while the averaged expressions are smooth for all times. |
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| ISSN: | 2158-3226 |