Stability of one‐dimensional boundary layers by using Green's functions
Emmanuel Grenier, Frédéric Rousset · Communications on Pure and Applied Mathematics · 2001
Abstract The aim of this paper is to investigate the stability of one‐dimensional boundary layers of parabolic systems as the viscosity goes to 0 in the noncharacteristic case and, more precisely, to prove that spectral stability implies linear and nonlinear stability of approximate solutions. In particular, we replace the smallness condition obtained by the energy method [10, 13] by a weaker spectral condition. © 2001 John Wiley & Sons, Inc.