## Global Solutions of the Compressible Navier-Stokes
Equations with Large Discontinuous Initial Data

#### Author: Gui-Qiang Chen, David Hoff, and Konstantina Trivisa

#### Title: Global Solutions of the Compressible Navier-Stokes Equations
with Large Discontinuous Initial Data

**Abstract** We prove the global existence of weak solutions to the
Navier-Stokes equations for compressible, heat-conducting flow in one
space dimension with large, discontinuous initial data, and we obtain
a-priori estimates for these solutions which are independent of time,
sufficient to determine their asymptotic behavior. In particular,
we show that, as time goes to infinity, the solution tends to a constant
state determined by the initial mass and the initial energy, and that
the magnitudes of singularities in the solution decay to zero.

This article has appeared in:

*Communications in Partial Differnetial Equations*,
**vol. 25(11&12)**, pages 2233-2257 (2000)

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