On the Inviscid Limit of the 3D Navier–Stokes Equations with Generalized Navier-Slip Boundary Conditions

Abstract

In this paper, we investigate the vanishing viscosity limit problem for the 3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded smooth domain of R 3 with the generalized Navier-slip boundary conditions (1.11). Some uniform estimates on rates of convergence in C([0, T ], L 2 (Ω)) and C([0, T ], H 1 (Ω)) of the solutions to the corresponding solutions of the idea Euler equations with the standard slip boundary condition are obtained.

Stability Analysis for the Incompressible Navier–Stokes Equations with Navier Boundary Conditions

“…Recently, [2] and the references therein give some more specified results on existence and regularity of the solutions for various domains. In addition, for results on the vanishing viscosity limit for the evolutionary case, see [29,30] and the references given by these authors. In 2016, Hailiang Li and Xingwei Zhang in [19] obtained the nonlinear stability for Couette flow of three dimensional compressible Navier-Stokes equations with Navier boundary conditions on the lower flat boundary and moving condition on the upper flat boundary in which the friction coefficient on the lower boundary is restricted to be negative.…”

Approximate Controllability for Navier–Stokes Equations in 3D Rectangles Under Lions Boundary Conditions

“…Lions boundary conditions are a particular case of Navier boundary conditions. For works and motivations concerning Lions and Navier boundary conditions (in both 2D and 3D cases) we refer to [6,10,11,16,30,31] and references therein.…”

Uniform regularity and vanishing viscosity limit for the compressible nematic liquid crystal flows

“…Recently, Masmoudi and Rousset [19] established conormal uniform estimates for three-dimensional general smooth domains with the Naiver-slip boundary condition and obtained convergence of the viscous solutions to the inviscid ones by a compact argument. Based on the uniform estimates in [9], better convergence with rates have been studied in [9] and [20]. In particular, Xiao and Xin [20] have proved the convergence in L ∞ (0, T ; H 1 ) with a rate of convergence.…”

“…Based on the uniform estimates in [9], better convergence with rates have been studied in [9] and [20]. In particular, Xiao and Xin [20] have proved the convergence in L ∞ (0, T ; H 1 ) with a rate of convergence. Motivated by the work of [19] and Xin [20], We [21] investigated the vanishing viscosity limit of incompressible nematic liquid crystal flows.…”