2013/05/18 by Benjamin Texier, Texier, Benjamin, Kevin Zumbrun +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1305.4275
openalex publication_date 2013/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a relative entropy condition recently shown by Leger and Vasseur\nto imply uniqueness and stable L2 dependence on initial data of Lax 1- or\nn-shock solutions of an n\× n system of hyperbolic conservation laws\nwith convex entropy implies Lopatinski stability in the sense of Majda. This\nmeans in particular that Leger and Vasseur's relative entropy condition\nrepresents a considerable improvement over the standard entropy condition of\ndecreasing shock strength and increasing entropy along forward Hugoniot curves,\nwhich, in a recent example exhibited by Barker, Freist "uhler and Zumbrun, was\nshown to fail to imply Lopatinski stability, even for systems with convex\nentropy. This observation bears also on the parallel question of existence, at\nleast for small BV or Hs perturbations\n