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arXiv · 1206.4119

On 3D Lagrangian Navier-Stokes $\alpha$ model with a Class of Vorticity-Slip Boundary conditions

Yuelong Xiao·Zhouping Xin
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Abstract

This paper concerns the 3-dimensional Lagrangian Navier-Stokes $\alpha$ model and the limiting Navier-Stokes system on smooth bounded domains with a class of vorticity-slip boundary conditions and the Navier-slip boundary conditions. It establishes the spectrum properties and regularity estimates of the associated Stokes operators, the local well-posedness of the strong solution and global existence of weak solutions for initial boundary value problems for such systems. Furthermore, the vanishing $\alpha$ limit to a weak solution of the corresponding initial-boundary value problem of the Navier-Stokes system is proved and a rate of convergence is shown for the strong solution.

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Yuelong Xiao, Zhouping Xin. 2012-06-19. On 3D Lagrangian Navier-Stokes $\alpha$ model with a Class of Vorticity-Slip Boundary conditions. https://doi.org/10.1007/s00021-012-0110-5

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