Global well-posedness of the velocity–vorticity-Voigt model of the 3D Navier–Stokes equations
| Autor: | Leo G. Rebholz, Yuan Pei, Adam Larios |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Curl (mathematics)
Applied Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Vorticity 01 natural sciences Physics::Fluid Dynamics 010101 applied mathematics Vorticity equation Inviscid flow Regularization (physics) Kelvin–Voigt material Periodic boundary conditions 0101 mathematics Navier–Stokes equations Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 266:2435-2465 |
| ISSN: | 0022-0396 |
| Popis: | The velocity–vorticity formulation of the 3D Navier–Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose a new regularization of the 3D Navier–Stokes equations, which we call the 3D velocity–vorticity-Voigt (VVV) model, with a Voigt regularization term added to momentum equation in velocity–vorticity form, but with no regularizing term in the vorticity equation. We prove global well-posedness and regularity of this model under periodic boundary conditions. We prove convergence of the model's velocity and vorticity to their counterparts in the 3D Navier–Stokes equations as the Voigt modeling parameter tends to zero. We prove that the curl of the model's velocity converges to the model vorticity (which is solved for directly), as the Voigt modeling parameter tends to zero. Finally, we provide a criterion for finite-time blow-up of the 3D Navier–Stokes equations based on this inviscid regularization. |
| Databáze: | OpenAIRE |
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