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

  • * Corresponding author

    * Corresponding author 

The first author is partially supported by NSF DMS 1522252 and ARO 65294-MA.
The second author is partially supported by NSF DMS 1522191 and ARO 65294-MA.
The third author is partially supported by NSF DMS 1418784.

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  • We study well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations, supplemented with no-slip velocity boundary conditions, a corresponding zero-normal condition for vorticity on the boundary, 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.

    Mathematics Subject Classification: Primary: 35Q30, 76N10.


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