Premium
Steady compressible Navier–Stokes equations with large potential forces via a method of decomposition
Author(s) -
Novotny Antonin,
Pileckas Konstantin
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19980525)21:8<665::aid-mma956>3.0.co;2-2
Subject(s) - mathematics , conservative vector field , compressibility , mathematical analysis , vector field , boundary value problem , bounded function , barotropic fluid , geometry , physics , mechanics
We investigate the steady compressible Navier–Stokes equations near the equilibrium state v = 0, ρ = ρ 0 ( v the velocity, ρ 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 (ρ 0 u ) = (0) and a compressible (irrotational) part ∇ϕ. 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 ϕ and a transport equation for the perturbation of the density σ = ρ − ρ 0 . For ρ 0 = 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. © 1998 B.G. Teubner Stuttgart–John Wiley & Sons Ltd.