One-dimensional flow of a compressible viscous micropolar fluid: a local existence theorem
One-dimensional flow of a compressible viscous micropolar fluid: a local existence theorem
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作者：
N. Mujakovic
研究了可压缩粘性导热微极流体一维流动的初边值问题。假定流体是热力学理想的多向流。证明了一个全局时间存在定理。证明是基于一个局部存在定理，在以前的文件[4]中获得。1.本文考虑可压缩粘性导热微极流体一维流动的初边值问题，它在热力学意义下是完全的和多向的（见[4]及参考文献）。设p、v、θ 1和e分别表示拉格朗日描述中的质量密度、速度、微旋转速度和温度。那么我们考虑的问题具有如下公式：op20V_ 0 ot + pox，ov 0（OV）0 t = ox Pox Kox（pe），pow =A[P~（pOW）_ 01]，ot ox oe 2 OV 2（OV）2 2（001）2 2 0（oe）PEii = -Kpe ox + pox + pox + 01 + Dpox Px（1.4）in ]0，1 [xR+，v（0，t）= v（1，t）= 0，01（0，t）= 01（1，t）= 0，oe oe ox（0，t）= ox（1，t）= 0，对于t ∈ R+，p（x，0）= Po（x），v（x，0）= vo（x），（1.5）（1.6）（1.第七章）
An initial-boundary value problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodinamicaly perfect and politropic. A global-in-time existence theorem is proved. The proof is based on a local existence theorem, obtained in the previous paper [4]. 1. Statement of the problem and the main result In this paper we consider an initial-boundary value problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid, being in thermodinamical sense perfect and politropic (see [4] and references therein). Let p, v, 01 and e denotes respectively the mass density, velocity, microrotation velocity and temperature in the Lagrangean description. Then the problem that we consider has the formulation as follows: op 20V _ 0 ot + p ox , ov 0 (OV) 0 t = ox P ox K ox(pe), pow =A[P~(pOW) _ 01], ot ox ox oe 2 OV 2(OV)2 2(001)2 2 0 ( oe) PEii = -Kp e ox + p ox + p ox + 01 + Dp ox P x (1.4) in ]0, l[xR+, v(O, t) = v(l, t) = 0, 01(0, t) = 01(1, t) = 0, oe oe ox (0, t) = ox (1, t) = 0, for t E R+, p(x, 0) = Po(x), v(x, 0) = vo(x), (1.5) (1.6) (1. 7)