Non-Uniqueness in Plane Fluid Flows
| Autor: | Gimperlein, Heiko, Grinfeld, Michael, Knops, Robin J., Slemrod, Marshall |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Quarterly of Applied Mathematics 82 (2024), 535-561 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/qam/1670 |
| Popis: | Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point produces an infinite number of solutions with the same initial data. Dafermos appeals to a maximal entropy rate criterion to recover uniqueness. These results are here interpreted as non-unique Lagrange trajectories on a particular spatial region. The corresponding velocity is proved consistent with plane steady compressible fluid flows that for specified pressure and mass density satisfy not only the Euler equations but also the Navier-Stokes equations for specially chosen volume and (positive) shear viscosities. The maximal entropy rate criterion recovers uniqueness. Comment: 25 pages, 10 figures, to appear in Quarterly of Applied Mathematics |
| Databáze: | arXiv |
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