[1] Matthews M T, Hill J M. Flow around nanospheres and nanocylinders. Quart J Mech Appl Math, 2006, 59:191-210 [2] Matthews M T, Hill J M. Newtonian flow with nonlinear Navier boundary condition. Acta Mechanica, 2007, 191:195-217 [3] Dussan V E B. The moving contact line:the slip boundary conditions. J Fluid Mech, 1976, 77:665-684 [4] Richardson S. On the no-slip boundary condition. J Fluid Mech, 1973, 59:707-719 [5] Navier C L M H. Sur les lois du mouvement des fluides. Mem Acad R Sci Inst Fr, 1827, 6:389-440 [6] Maxwell J C. On stresses in rarefied gases arising from inequalities of temperature. Phil Trans R Soc London, 1879, 170:231-256 [7] Amrouche C, Rejaiba A. Navier-Stokes equations with Navier boundary condition. Math Methods Appl Sci, 2016, 39(17):5091-5112 [8] Beirão da Veiga, Crispo F. The 3-D inviscid limit result under slip boundary conditions, A negative answer. J Math Fluid Mech, 2012, 14(1):55-59 [9] Iftimie D, Sueur F. Viscous boundary layers for the Navier-Stokes equations with the Navier slip conditions. Arch Ration Mech Anal, 2011, 199(1):145-175 [10] Jager W, Mikelić A. On the roughness-induced effective boundary conditions for an incompressible viscous flow. J Differential Equations, 2001, 170(1):96-122 [11] Kashiwabara T. On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type. J Differential Equations, 2013, 254(2):756-778 [12] Xiao Y L, Xin Z P. On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition. Comm Pure Appl Math, 2007, 60(7):1027-1055 [13] Xiao Y L, Xin Z P. On 3D Lagrangian Navier-Stokes α model with a class of vorticity-slip boundary conditions. J Math Fluid Mech, 2013, 15(2):215-247 [14] Zajaczkowski W M. Global special regular solutions to the Navier-Stokes equations in a cylindrical domain without the axis of symmetry. Topol Methods Nonlinear Anal, 2004, 24(1):69-105 [15] Zhong X. Vanishing viscosity limits for the 3D Navier-Stokes equations with a slip boundary condition. Proc Amer Math Soc, 2017, 145(4):1615-1628 [16] Masmoudi N, Rousset F. Uniform regularity for the Navier-Stokes equation with Navier boundary condition. Arch Ration Mech Anal, 2012, 203(2):529-575 [17] Clopeau T, Mikelić A, Robert R. On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions. Nonlinearity, 1998, 11(6):1625-1636 [18] Lopes Filho M C, Nussenzveig Lopes H J, Planas G. On the inviscid limit for two-dimensional incompressible flow with Navier friction condition. SIAM J Math Anal, 2005, 36(4):1130-1141 [19] Kelliher J P. Navier-Stokes equations with Navier boundary conditions for a bounded domain in the plane. SIAM J Math Anal, 2006, 38(1):210-232 [20] Lions J L. Quelques Methodes de Resolution des Problemes aux Limites non Lineaires. Dunod; GauthierVillars, Paris, 1969 [21] Beirão da Veiga H, Crispo F. Sharp inviscid limit results under Navier type boundary conditions:An Lp theory. J Math Fluid Mech, 2010, 12(3):397-411 [22] Temam R. Navier-Stokes Equations. Amsterdam:North-Holland, 1979 [23] Sohr H. The Navier-Stokes Equations. An Elementary Functional Analytic Approach, Modern Birkhauser Classics. Basel:Birkhauser/Springer Basel AG, 2001 [24] Necas J. Direct Methods in the Theory of Elliptic Equations. Springer, 2012 |