Remarks about the Inviscid Limit of the Navier–Stokes System

By Nader Masmoudi. 2007

213 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/755ebbbea8e97bcec404eb146f89f731cd5f1f7f

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Vanishing Viscous Limits for 3D Navier–Stokes Equations with a Navier-Slip Boundary Condition (2012, methodology): “In the absence of physical boundaries, then any smooth solutions to the Euler system can be approximated by the ones to Navier–Stokes equations, see [2,9,10,12,16,17,20,30].”
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, background): “In the case of the whole space (or the case there is no boundary) this approach yields a uniform time of existence and the convergence towards a solution of the Euler system (see [35, 18, 26]).”
On the Euler equations of incompressible fluids (2007, background): “as the solution remains in the same space ([108]).”
Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption (2020, background): “Without boundary effect, the mathematical theories are now satisfactory (see, for instance, [7,27] and references therein).”
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations (2012, methodology): “When there is no boundary, the vanishing viscosity limit can be justified by using the three types of methods: we refer to Swann [51] and Kato [31] (see also [39]) for results with the first approach, to DiPerna and Majda [16, 15] for the second approach in the two-dimensional case and to the book [”
Weak-Strong Uniqueness for Measure-Valued Solutions (2009, background): “Known results in the literature about the convergence of solutions of Navier-Stokes to Euler (see for instance [5, 12]) assume more regularity.”
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 the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane (2012, unknown): “[8, 6, 9, 22].”
Concerning the Wk,p-Inviscid Limit for 3-D Flows Under a Slip Boundary Condition (2011, background): “See, for instance, [15,25–27,30,38], and the more recent papers [8, 32 ] (in [8,25,32] results are proved in strong topology).”