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2018, Volume 38, Issue 7: 3459-3477. Doi: 10.3934/dcds.2018148
This issue Previous Article Non-floquet invariant tori in reversible systems Next Article Sturm 3-ball global attractors 3: Examples of Thom-Smale complexes

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

  • 1.

    Department of Mathematics, University of Houston, Houston, TX, 77204, USA

  • 2.

    Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA

  • 3.

    Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA

  • * 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.

Received:  July 2017
Revised:  February 2018
Published:  July 2018
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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 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.

    Citation:
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