On the vanishing viscosity limit for the 3D Navier‐Stokes equations with a slip boundary condition

By Yue-long Xiao, Zhouping Xin. 2007

291 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f6f8a5d29aa1ec503583463f351c52bd75dce924

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods (2012, background): “Let us also mention that when considered in the whole space [28, 12, 19] or with other boundary conditions such as Navier boundary condition [32, 11, 2, 20] or incoming flow [30], the convergence problem becomes simpler since there is no boundary layer or the boundary layer is stable.”
Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition (2010, unknown): “For some special Navier boundary conditions considered in [39, 5, 4, 6], the leading profile V vanishes and hence uniform H3 or W 2,p, p > 3 estimates have been obtained.”
Concerning the Wk,p-Inviscid Limit for 3-D Flows Under a Slip Boundary Condition (2011, background): “[ 42 ] may lead to the more stringent results stated in Theorem 1.2 in the particular case p =2 .”
Boundary layer associated with the Darcy–Brinkman–Boussinesq model for convection in porous media (2011, background): “There is an abundant literature on boundary layer associated with incompressible flows and the related question of vanishing viscosity (see for instance [2, 6, 46, 47, 9, 39, 14, 22, 45, 19, 20, 7, 27, 68, 30, 3, 4, 32, 29, 65, 1, 66, 21, 55, 56, 51, 53, 54, 59, 23, 8, 25, 18, 26, 18, 26, 37, 5, 15,”
Initial–boundary value problems for a system of hyperbolic balance laws arising from chemotaxis (2015, unknown): “[22,31]).”
Viscous boundary layers for the Navier–Stokes equations with the Navier slip conditions (2011, background): “As a consequence they extend the boundary condition ω = 0 on ∂Ω which was considered by J.L. Lions in [27] p. 87-98, P.L. Lions in [28] p. 129-131, Xiao and Xin in [38], Ziane in [39].”