Multidimensional Stability of Large-Amplitude Navier–Stokes Shocks
Multidimensional Stability of Large-Amplitude Navier–Stokes Shocks
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DOI：
10.1007/s00205-017-1147-7
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发表时间：
2017-07
影响因子：
2.5
通讯作者：
J. Humpherys;Gregory Lyng;K. Zumbrun
中科院分区：
文献类型：
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作者：
J. Humpherys;Gregory Lyng;K. Zumbrun
将Humphys-Lyng-Zumbrun的结果推广到一维情形，我们使用渐近常微分方程组估计和数值Evans函数计算相结合的方法，考察了平面Navier-Stokes激波在各种激波振幅范围内的多维稳定性，包括无限幅极限、单原子或双原子理想气体状态方程、粘性系数和热传导系数、常数以及统计力学预测的物理比和马赫数。我们的结果表明在所考虑的参数范围内是无条件稳定的；这与Erpenbeck和Majda对于相应的无粘欧拉激波的结果是一致的。值得注意的是，这项研究首次成功地对与粘性激波的多维稳定性有关的埃文斯函数进行了数值计算。所介绍的方法原则上可以用来确定在任何多变气体中的激波的稳定性，或者实际上对于其他模型的激波，特别是包括粘弹性、燃烧和磁流体动力学(MHD)的激波。
Extending results of Humpherys–Lyng–Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier–Stokes shocks across the full range of shock amplitudes, including the infinite-amplitude limit, for monatomic or diatomic ideal gas equations of state and viscosity and heat conduction coefficients,, andconstant and in the physical ratios predicted by statistical mechanics, and Mach number. Our results indicate unconditional stability within the parameter range considered; this agrees with the results of Erpenbeck and Majda for the corresponding inviscid case of Euler shocks. Notably, this study includes the first successful numerical computation of an Evans function associated with the multidimensional stability of a viscous shock wave. The methods introduced can be used in principle to decide stability for shocks in any polytropic gas, or indeed for shocks of other models, including in, particular, viscoelasticity, combustion, and magnetohydrodynamics (MHD).