Global Weak Solutions to 1D Compressible Isentropic Navier-Stokes Equations with Density-Dependent Viscosity
Global Weak Solutions to 1D Compressible Isentropic Navier-Stokes Equations with Density-Dependent Viscosity
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DOI：
10.4310/maa.2005.v12.n3.a2
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发表时间：
2005-09
影响因子：
0.3
通讯作者：
Song Jiang;Z. Xin;Ping Zhang
中科院分区：
文献类型：
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作者：
Song Jiang;Z. Xin;Ping Zhang
由于在真空处的强简并性，可压缩流体的欧拉系统和纳维 - 斯托克斯系统（其中黏度与密度无关）都呈现出奇异性[7, 10, 16]。特别地，经典的一维等熵纳维 - 斯托克斯系统对于最初由真空态分隔的两种气体得到了非物理的解[7, 10]。为了克服这一困难，刘、辛和杨在[10]中引入了修正的纳维 - 斯托克斯系统(1.1)，其中黏度系数依赖于密度。在[10]中表明，至少在局部时间内，系统(1.1)产生了具有物理相关性的解。正如刘、辛和杨在[10]中所指出的，该模型也是由物理考虑所推动的，即在从玻尔兹曼方程推导可压缩纳维 - 斯托克斯方程时，黏度不是常数且依赖于温度。对于等熵流，这种依赖性转化为黏度对密度的依赖性。为了简单起见，我们在本文中考虑……
Due to the strong degeneracy at vacuum, both Euler and Navier-Stokes systems for compressible fluids (in which the viscosity is independent of density) behave singularly [7, 10, 16]. In particular, the classical one-dimensional isentropic Navier-Stokes system picks up unphysical solutions for two gases initially separated by vacuum states [7, 10]. To overcome this difficulty, Liu, Xin and Yang in [10] introduced the modified Navier-Stokes system (1.1) in which the viscosity coefficient depends on the density. It is shown in [10] that at least locally in time, the system (1.1) yields the physically relevant solution. As remarked by Liu, Xin and Yang in [10], the model is also motivated by the physical consideration that in the derivation of the compressible Navier-Stokes equations from the Boltzmann equations, the viscosity is not constant and depends on the temperature. For isentrpoic flow, this dependence is translated into the dependence of the viscosity on the density. For simplicity we consider in this paper