TAILIEUCHUNG - Báo cáo sinh học: " Research Article One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 796065 21 pages doi 2010 796065 Research Article One-Dimensional Compressible Viscous Micropolar Fluid Model Stabilization of the Solution for the Cauchy Problem Nermina Mujakovic Department of Mathematics University of Rijeka Omladinska 14 51000 Rijeka Croatia Correspondence should be addressed to Nermina Mujakovic mujakovic@ Received 8 November 2009 Revised 24 May 2010 Accepted 1 June 2010 Academic Editor Salim Messaoudi Copyright 2010 Nermina Mujakovic. 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. 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 Rx 0 T for each T 0. Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of T which we use in proving of the stabilization of the solution. 1. Introduction In this paper we consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid. It is assumed that the fluid is thermodynamically perfect and polytropic. The same model has been considered in 1 2 where the global-in-time existence and uniqueness for the generalized solution of the problem on Rx 0 T T 0 are proved. Using the results from 1 3 we can also easily conclude that the mass density and temperature are strictly positive. Stabilization of the solution of the Cauchy problem for the classical fluid where microrotation is equal to zero has been considered in 4 5 . In 4 was analyzed the Holder continuous solution. In 5 is considered the special case of our problem. We use here some .

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