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| Hovedforfatter: | |
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| Format: | Recurso digital |
| Sprog: | engelsk |
| Udgivet: |
Zenodo
2025
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| Fag: | |
| Online adgang: | https://doi.org/10.2139/ssrn.5295963 |
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Indholdsfortegnelse:
- <p><span lang="EN-US">This paper presents a complete structural validation of bounded Couette flow under the Enhanced VES (E–VES) framework—a recent filtering formalism that classifies steady viscous flows based on three non-negotiable criteria: global energy closure, functional admissibility in Sobolev spaces, and geometric domain consistency. While Couette flow is traditionally regarded as non-paradoxical and physically canonical, its admissibility has never been explicitly demonstrated within a rigorous mathematical structure. This work fills that gap.</span></p> <p><span lang="EN-US">We consider the classical configuration of planar Couette flow confined between two rigid, parallel plates, with the upper plate moving at constant speed and the lower held stationary. The velocity field is derived from first principles and shown to satisfy the steady Navier–Stokes equations in the absence of pressure gradients. We then explicitly verify the global energy identity: the mechanical work performed by the boundary matches the viscous dissipation in the fluid volume. Functional regularity is established by proving that the velocity field belongs to </span><span></span><span lang="EN-US">, with exact norm estimates. Geometric admissibility is confirmed via the boundedness and closure of the physical domain.</span></p> <p><span lang="EN-US">These results demonstrate that bounded Couette flow satisfies all E–VES criteria without exception or approximation. The analysis not only validates this classical solution but also affirms the precision of the E–VES framework: it excludes structurally inconsistent flows without discarding physically essential ones. This work thereby provides a foundational benchmark for future admissibility studies involving both canonical and composite shear-driven configurations.</span></p>