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Báo cáo hóa học: " Global existence of strong solutions to the micropolar, compressible flow with density-dependent viscosities"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Global existence of strong solutions to the micropolar, compressible flow with density-dependent viscosities | Chen Boundary Value Problems 2011 2011 13 http www.boundaryvalueproblems.eom content 2011 1 13 RESEARCH o Boundary Value Problems a SpringerOpen Journal Open Access Global existence of strong solutions to the micropolar compressible flow with density-dependent viscosities Mingtao Chen1 2 Correspondence mtchen@sdu.edu. cn 1College of Mathematical Sciences Xiamen University Xiamen 361005 PR China Full list of author information is available at the end of the article Abstract This article is concerned with global strong solutions of the micro-polar compressible flow with density-dependent viscosity coefficients in one-dimensional bounded intervals. The important point in this article is that the initial density may vanish in an open subset. 1 Introduction Theory of micro-polar compressible flow was first introduced by Eringen 1 describing the compressible fluids with randomly oriented particles suspended in the medium when the deformation of fluid particles is ignored. The governing equations in Eulerian coordinate take the form as Pt p u x 0 pu t pu2 x px pUx x p w t puw x 2vw ẢWx x pe t peu x pUx p Ux 2 Ấ Wx 2 2pw2 kỡx x 1 where p p t x denotes the density of the fluid u u t x is the velocity w w t x is the micro-rotational velocity 0 0 t x is the temperature e e t x is the internal energy p p p 0 is the pressure. p p p 0 V V p 0 and l l p 0 are the viscosities of the fluid and K is the heat conductivity. There are several articles that have considered the above micro-polar compressible flow with the viscosity being constant satisfying some physical meaning. Here we only refer the reader to 2-4 wherein the global existence was established for 1 with the condition that the initial density needs to be bounded a way from zero. In view of their being physically important the viscosities are not constants. In this article we consider a simpler model 2 below. For the physical consideration in the case of isothermal flow 5 introduce the viscosities depending on the density