Contact discontinuity with general perturbations for gas motions
Contact discontinuity with general perturbations for gas motions
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DOI：
10.1016/j.aim.2008.06.014
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发表时间：
2008-11
影响因子：
1.7
通讯作者：
F. Huang;Z. Xin;Tong Yang
中科院分区：
文献类型：
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作者：
F. Huang;Z. Xin;Tong Yang
接触间断是气体运动的基本波型之一。Navier-Stokes方程和Boltzmann方程在一般扰动下接触间断的稳定性是一个长期存在的问题。一般扰动的接触不连续性可能会产生扩散波的发展和相互作用的接触波，造成分析困难。本文成功地得到了Navier-Stokes方程和Boltzmann方程的具有一致收敛速度的接触波斑图的大时间渐近稳定性。其中一个关键的观察结果是，即使解与接触波的偏差的能量范数可能以（1+t）14的速率增长，它也可以通过偏差的导数的能量范数的衰减来补偿，其数量级为（1+t）-14。因此，扰动随时间演化的衰减率的倒数阶对于关闭包含低阶估计的L∞范数的一致界的先验估计是必不可少的，然后它给出了接触波图案解的衰减。
The contact discontinuity is one of the basic wave patterns in gas motions. The stability of contact discontinuities with general perturbations for the Navier–Stokes equations and the Boltzmann equation is a long standing open problem. General perturbations of a contact discontinuity may generate diffusion waves which evolve and interact with the contact wave to cause analytic difficulties. In this paper, we succeed in obtaining the large time asymptotic stability of a contact wave pattern with a convergence rate for the Navier–Stokes equations and the Boltzmann equation in a uniform way. One of the key observations is that even though the energy norm of the deviation of the solution from the contact wave may grow at the rate (1+t)14, it can be compensated by the decay in the energy norm of the derivatives of the deviation which is of the order of (1+t)−14. Thus, this reciprocal order of decay rates for the time evolution of the perturbation is essential to close the a priori estimate containing the uniform bounds of the L∞norm on the lower order estimate and then it gives the decay of the solution to the contact wave pattern.