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