One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem

Boundary Value Problems20102010:796065

DOI: 10.1155/2010/796065

Received: 8 November 2009

Accepted: 1 June 2010

Published: 24 June 2010

Abstract

We consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on http://static-content.springer.com/image/art%3A10.1155%2F2010%2F796065/MediaObjects/13661_2009_Article_956_IEq1_HTML.gif for each http://static-content.springer.com/image/art%3A10.1155%2F2010%2F796065/MediaObjects/13661_2009_Article_956_IEq2_HTML.gif . Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of http://static-content.springer.com/image/art%3A10.1155%2F2010%2F796065/MediaObjects/13661_2009_Article_956_IEq3_HTML.gif , which we use in proving of the stabilization of the solution.

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Authors’ Affiliations

(1)
Department of Mathematics, University of Rijeka

Copyright

© Nermina Mujaković. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.