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Open Access Research

3-D flow of a compressible viscous micropolar fluid with spherical symmetry: a local existence theorem

Ivan Dražić1* and Nermina Mujaković2

Author affiliations

1 Faculty of Engineering, University of Rijeka, Rijeka, Croatia

2 Department of Mathematics, University of Rijeka, Rijeka, Croatia

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Citation and License

Boundary Value Problems 2012, 2012:69  doi:10.1186/1687-2770-2012-69

Published: 2 July 2012

Abstract

We consider nonstationary 3-D flow of a compressible viscous heat-conducting micropolar fluid in the domain to be the subset of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/69/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/69/mathml/M1">View MathML</a> bounded with two concentric spheres that present solid thermoinsulated walls. In thermodynamical sense fluid is perfect and polytropic. Assuming that the initial density and temperature are strictly positive we will prove that for smooth enough spherically symmetric initial data there exists a spherically symmetric generalized solution locally in time.

Keywords:
micropolar fluid; generalized solution; spherical symmetry; weak and strong convergence