“…The established techniques used for finding existence and regularity for the incompressible model may be divided into two groups: classical PDE techniques for surfaces of prescribed mean curvature, as, for example, in [Ladyzhenskaya and Ural'tseva 1970;Huisken 1985;Gilbarg and Trudinger 2001, Chapter 16]; and functions of bounded variation and sets of finite perimeter setting for minimizing the energy, as, for example, in [Emmer 1973;Gerhardt 1974;Giusti 1980;Gonzalez et al 1980;Huisken 1985]. In contrast, results concerned with compressible liquids are very recent and comparatively few [Athanassenas and Finn 2006;Finn and Luli 2007].…”