An L(p)-Theory for the n-Dimensional, Stationary, Compressible, Navier-Stokes Equations, and the Incompressible Limit for Compressible Fluids. The Equilibrium Solutions.

Abstract

This paper studies a system which describes the stationary motion of a given amount of a compressible heat conducting, viscous fluid in a bounded domain omega of R sub n, n > 2. Here u(x) is the velocity field, rho(x) is the density of the fluid, zeta(x) is the absolute temperature, f(x) and h(x) are the assigned external force field and heat sources per unit mass, and p(rho, zeta) is the pressure. In the physically significant case one has g = 0. We prove that for small data (f,g,h) there exists a unique solution (u, rho, zeta) of the problem in a neighborhood of (0, m, zeta sub 0); for arbitrarily large data the stationary solution does not exist in general. Moreover, we prove that (for barotropic flows) the stationary solution of the compressible Navier-Strokes equations, as the Mach number becomes small. Section 5 studies the equilibrium solutions for the system. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1986
Accession Number
ADA172778

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  • H. Beirao Da Veiga

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  • University of Wisconsin–Madison

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  • C4I

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