Steady compressible Navier–Stokes equations with large potential forces via a method of decomposition

✍ Scribed by Antonin Novotny; Konstantin Pileckas

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 158 KB
• Volume: 21
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19980525)21:8<665::aid-mma956>3.0.co;2-2

✦ Synopsis

Communicated by Y. Shibata

We investigate the steady compressible Navier-Stokes equations near the equilibrium state v"0, " (v the velocity, the density) corresponding to a large potential force. We introduce a method of decomposition for such equations: the velocity field v is split into a non-homogeneous incompressible part u (div ( u)"0) and a compressible (irrotational) part . In such a way, the original complicated mixed elliptic-hyperbolic system is split into several 'standard' equations: a Stokes-type system for u, a Poisson-type equation for and a transport equation for the perturbation of the density " ! . For "const. (zero potential forces), the method coincides with the decomposition of Novotny and Padula [21]. To underline the advantages of the present approach, we give, as an example, a 'simple' proof of the existence of isothermal flows in bounded domains with no-slip boundary conditions. The approach is applicable, with some modifications, to more complicated geometries and to more complicated boundary conditions as we will show in forthcoming papers.