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Global Solutions to the Navier-Stokes Equations for Compressible
Heat-Conducting Flow with Symmetry and Free Boundary

#### Authors: Gui-Qiang Chen and Milan Kratka

#### Title:
Global Solutions to the Navier-Stokes Equations for Compressible
Heat-Conducting Flow with Symmetry and Free Boundary

**Abstract**

Global solutions of the multidimensional Navier-Stokes equations for
compressible heat-conducting flow are constructed, with spherically
symmetric initial data of large oscillation between a static solid core
and a free boundary connected to a surrounding vacuum state.
The free boundary connects the compressible heat-conducting fluids
to the vacuum state with free normal stress and zero normal heat flux.
The fluids are initially assumed to fill with a finite volume and zero
density at the free boundary, and with bounded positive density and
temperature between the solid core and the initial position of the
free boundary.
One of the main features of this problem is the singularity of solutions
near the free boundary.
Our approach is to combine an effective difference scheme to construct
approximate solutions with the energy methods and the pointwise estimate
techniques to deal with the singularity of solutions near the free
boundary and to obtain the bounded estimates of the solutions and the
free boundary as time evolves.
The convergence of the difference scheme is established.
It is also proved that no vacuum develops between the solid core and
the free boundary, and the free boundary expands with finite speed.

This article has appeared in:

*Communications in Partial Differential Equations* ** vol. ??**,
pages ?? (2002)

This paper is available in the following formats:

A closely related paper is Change me.

**Author Address**
Gui-Qiang Chen
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
gqchen@math.nwu.edu