Secchi, Paolo On a stationary problem for the compressible Navier-Stokes equations: The self-gravitating equilibrium solutions. (English) Zbl 0818.35080 Differ. Integral Equ. 7, No. 2, 463-482 (1994). A stationary system for compressible, viscous and heat-conductive fluid in a bounded three-dimensional domain in a self-induced gravitational potential field is studied. For vanishing external forces and heat sources it is proved that there exists an equilibrium solution, i.e. such a triple (velocity, pressure, temperature) that the velocity equals zero. When the gravitational constant approaches zero, this equilibrium solution is shown to become spatially constant. Reviewer: T.Roubíček (Praha) Cited in 4 Documents MSC: 35Q30 Navier-Stokes equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics Keywords:compressible viscous fluid; self-induced gravitation; stationary equilibrium PDFBibTeX XMLCite \textit{P. Secchi}, Differ. Integral Equ. 7, No. 2, 463--482 (1994; Zbl 0818.35080)