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arXiv · 1708.02241

On well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations with no-slip boundary conditions

Maxim A. Olshanskii·Leo G. Rebholz·Abner J. Salgado
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Abstract

We study well-posedness of a velocity-vorticity formulation of the Navier--Stokes equations, supplemented with no-slip velocity boundary conditions, a no-penetration vorticity boundary condition, along with a natural vorticity boundary condition depending on a pressure functional. In the stationary case we prove existence and uniqueness of a suitable weak solution to the system under a small data condition. The topic of the paper is driven by recent developments of vorticity based numerical methods for the Navier--Stokes equations.

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Maxim A. Olshanskii, Leo G. Rebholz, Abner J. Salgado. 2017-08-07. On well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations with no-slip boundary conditions. https://arxiv.org/abs/1708.02241

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