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

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.

To appear in J. Math. Fluid Mech

References in corpus (3)

• A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations
• The Three Dimensional Viscous Camassa-Holm Equations, and Their Relation to the Navier-Stokes Equations and Turbulence Theory
• Length-scale estimates for the LANS-alpha equations in terms of the Reynolds number

Cited by in corpus (4)

• Incompressible limit of strong solutions to 3-D Navier-Stokes equations with Navier's slip boundary condition for all time
• Vanishing Viscosity Limit For the 3D Nonhomogeneous Incompressible Navier-Stokes Equations With a Slip Boundary Condition
• Stochastic model error in the LANS-alpha and NS-alpha deconvolution models of turbulence
• Zero kinematic viscosity-magnetic diffusion limit of the incompressible viscous magnetohydrodynamic equations with Navier boundary conditions