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# Accession Number:

## ADA172778

# Title:

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

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Report Date:

## 1986-06-01

# Pagination or Media Count:

##
33.0

# 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 ux is the velocity field, rhox is the density of the fluid, zetax is the absolute temperature, fx and hx are the assigned external force field and heat sources per unit mass, and prho, 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#