Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation

By E. Weinan. 2000

201 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/3a93ea5593174303ac6af965312350580754e28d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A note on Prandtl boundary layers (2010, background): “For further mathematical results, see the review paper [1].”
Well-posedness of the Prandtl equation in Sobolev spaces (2012, background): “For the related mathematical results and discussions, also see the review papers [2, 4].”
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,”
Recent progresses in boundary layer theory (2015, unknown): “, [10, 15, 24, 28, 80, 82, 84, 86, 96, 100, 109, 111, 112, 125, 131].”
A Kato type theorem on zero viscosity limit of Navier-Stokes flows (2001, methodology): “One of the fundamental system governing the motion of fluids like air and water under normal conditions is the Navier-Stokes equations for incompressible homogeneous Newtonian fluids: ∂u ∂t + (u · ∇)u − ν∆u +∇p = f , in Ω, (1) div u = 0 in Ω, (2) u = b on Γ, (3) u = u0 at t = 0, (4) where u = (u1, u”
On the Euler equations of incompressible fluids (2007, background): “Boundary layers are very real but difficult to study rigorously, especially if the domains are curved and the flows are time-dependent ([23], [24], [74], [75]).”
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations (2012, background): “Nevertheless, in the presence of boundaries, the situation can be more complicated, as we shall describe below (we refer for example to the review articles [16,24] for more details).”
Boundary Layers Associated with Incompressible Navier–Stokes Equations: The Noncharacteristic Boundary Case (2002, background): “See also the survey paper by Weinan E [11].”
On the local existence of analytic solutions to the Prandtl boundary layer equations (2013, unknown): “For a complete survey of the mathematical and numerical results on the Prandtl boundary layer equations, we refer the reader to [4, 9, 11, 29].”