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

TL;DR

This paper studies the 3D Lagrangian Navier-Stokes alpha model with vorticity-slip boundary conditions, establishing spectral properties, well-posedness, and convergence to classical Navier-Stokes solutions as alpha approaches zero.

Contribution

It introduces new analysis of the Lagrangian Navier-Stokes alpha model with vorticity-slip boundaries, including spectral, regularity, and convergence results.

Findings

Spectral properties and regularity estimates of Stokes operators.

Local well-posedness and global existence of solutions.

Convergence of the alpha model to Navier-Stokes solutions as alpha vanishes.

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.