On the inviscid limit of the Navier-Stokes equations

By Peter Constantin, Igor Kukavica, Vlad Vicol. 2014

85 citations recorded by the source corpus.

We consider the convergence in the L 2 norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow, and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer, then the inviscid limit holds.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/c07907777966d90d79e0af87991c222465ccced2

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

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.”
The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space (2017, background): “rgy norm if and only if the energy dissipation near the boundary vanishes in the inviscid limit: precisely ν Z T 0 ZZ {z.ν} |∇u|2 dxdzdt −→ 0, as ν→ 0. (1.4) See also its many variants: for instance, [3, 5, 6, 7, 24], among others. In this paper, we give a direct proof of the inviscid limit for data”
Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods (2012, background): “This criterion was extended in different directions (see [5, 19, 36, 38]).”