On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary
On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary
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DOI：
10.18910/10064
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发表时间：
2004-03
影响因子：
0.4
通讯作者：
F. Huang;A. Matsumura;Xiaoding Shi
中科院分区：
文献类型：
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作者：
F. Huang;A. Matsumura;Xiaoding Shi
式中（）为速度，ρ() >为密度，θ（）为绝对温度，μ > 0为粘度常数，κ > 0为热传导系数。压强= (ρ θ)和热力学能= (ρ θ)是由热力学第二定律联系起来的。对于系统（1.1）解的渐近行为已经有很多研究。这些结果大多与稀薄波和粘性激波有关。2 × 2病例参考文献[10-15]，3 × 3病例参考文献[4 - 5,7 - 8]。然而，由于各种困难，直到现在还没有关于系统（1.1）接触不连续的结果。虽然Liu和Xin[9]和Xin[17]在接触不连续问题上取得了一些进展，研究了具有均匀人工黏度的黏性守恒定律的初值问题（IVP）的接触不连续渐近性，但对于物理系统，特别是可压缩N-S方程（1.1）没有结果。因此，我们确实希望给出物理系统（1.1）接触不连续的肯定结果。为了简化问题，我们把注意力集中在完美气体上。在这种情况下，
where ( ) is the velocity, ρ( ) > 0 the density, θ( ) the absolute temperature, μ > 0 the viscosity constant and κ > 0 the coefficient of heat conduction. The pressure = (ρ θ) and the internal energy = (ρ θ) are related by the second law of thermodynamics. There have been a lot of works on the asymptotic behaviors of the solutions for the system (1.1). Most of these results are concerned with the rarefaction wave and viscous shock wave. We refer to [10–15] for 2 × 2 case and [4–5, 7–8] for 3 × 3 case and references therein. However there is no result on the contact discontinuity for the system (1.1) until now due to various difficulties. Although some progress on the contact discontinuity were obtained by Liu and Xin [9] and Xin [17] in which the asymptotic toward the contact discontinuity was investigated for the initial value problem (IVP) of viscous conservation laws with uniformly artificial viscosity, no result is known for the physical system, especially for the compressible N-S equations (1.1). Therefore we really want to give a positive result on the contact discontinuity for the physical system (1.1). To simplify our problem, we focus our attention on the perfect gas. In this situation,