Global existence and stability to the polytropic gas dynamics with an outer force
Global existence and stability to the polytropic gas dynamics with an outer force
复制标题
外力作用下多变气体动力学的整体存在性和稳定性
DOI：
10.1016/j.aml.2019.03.022
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发表时间：
2019
影响因子：
3.7
通讯作者：
Naoki Tsuge
中科院分区：
文献类型：
--
作者：
Yan-bo Hu a;Yun-guang Lu;Naoki Tsuge
本文利用粘流近似方法和极大值原理，得到了具有外力作用的可压缩多方气体动力学方程组近似解的先验L∞估计，并证明了当绝热指数γ> 1时熵解的整体存在性.目前的问题是经典的，很久以前就知道整体存在。然而，L∞估计相对于时间变量变得更大。因此，它不能保证解决方案的稳定性。因此，我们证明了关于时间变量的一致L∞估计。我们的解决方案是稳定的。其关键思想是采用一个不变的区域取决于空间和时间变量。这种方法使我们能够详细研究解的行为，并推导出所需的估计。
In this paper, we apply the viscosity-flux approximation method coupled with the maximum principle to obtain the a-priori L∞ estimates for the approximation solutions of the compressible polytropic gas dynamics system with an outer force, and prove the global existence of entropy solutions for any adiabatic exponent γ> 1. The present problem was classical and the global existence was known long ago. However, the L∞ estimates grow larger with respect to the time variable. As a result, it does not guarantee the stability of solutions. We thus prove the uniformly L∞ estimate with respect to the time variable. This means that our solutions are stable. The key idea is to employ an invariant region depending on the space and time variables. This method enables us to investigate the behavior of solutions in detail and deduce the desired estimates.