Stability of one‐dimensional boundary layers by using Green's functions

By E. Grenier, Frédéric Rousset. 2001

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Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition (2010, unknown): “We refer for example to [38], [10], [9], [32], [11, 24], [12], [31], [27], [30].”
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations (2012, background): “The constuction and justification of the asymptotic expansion, even for general hyperbolic-parabolic systems have been widely studied recently, we refer to [21, 23, 24, 41, 26, 45, 54].”
Boundary Layer Stability¶in Real Vanishing Viscosity Limit (2001, background): “On the contrary, a recent work by Grenier and Rousset [ 13 ] shows that spectral stability of the boundary layer implies non-linear stability, under the condition that r = n. Let us give a short description of their result.”
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames (2004, methodology): “in [15], the stability of viscous boundary layers is investigated through a Green’s functions approach – an approach initiated by Zumbrun and Howard [25] for the study of the stability of travelling waves for viscous systems of conservation laws.”