A Kato type theorem on zero viscosity limit of Navier-Stokes flows

By Xiaoming Wang. 2001

140 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/59a5477c1141c5d68864651e68c4c4faa2673cc4

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

On the Inviscid Limit for the Compressible Navier–Stokes System in an Impermeable Bounded Domain (2012, unknown): “Furthermore there exists many variants of Kato’s argument: see for instance [35, 26, 21].”
Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods (2012, background): “…of the underlying physical domain T×R+ allows certain quantities growth at y = +∞ even if the solution is smooth or bounded in Hs; (iii) the lack of higher order boundary conditions at y = 0 prevents us to apply the integration by parts in the variable y, but it is a standard and…”
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,”
On Kato's conditions for vanishing viscosity (2007, background): “Temam and Wang in [3] and [5] show that, at the expense of increasing the size of the boundary layer slightly, one need only consider the tangential derivatives of the tangential components of the velocity or the tangential derivatives of the normal components of the velocity.”
The Inviscid Limit for the Navier–Stokes Equations with Data Analytic Only Near the Boundary (2019, methodology): “Refinements and extensions based on Kato’s original argument of introducing a boundary layer corrector were obtained for instance in [3, 6, 7, 31, 33, 46, 54, 56]; see also the recent review [45] and references therein.”
Vanishing Viscous Limits for 3D Navier–Stokes Equations with a Navier-Slip Boundary Condition (2012, methodology): “While for general curved domains, due to the curvature of ∂Ω, u does not vanish in general, which leads to new difficulties in the estimates of derivatives by the methods in [12, 31, 3, 4, 30, 32].”
On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane (2012, background): “On the other hand, the necessary and sufficient condition for theL(2) convergence of the Navier-Stokes flows to the Euler flows was given by [25], which was extended by several authors [26, 27, 53, 55].”