On the long-time behavior of solution for compressible Navier-Stokes system with outflow boundary condition
On the long-time behavior of solution for compressible Navier-Stokes system with outflow boundary condition
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DOI：
10.1016/j.jde.2022.03.033
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发表时间：
2022-06
影响因子：
2.4
通讯作者：
Ten-See Wang
中科院分区：
文献类型：
--
作者：
Ten-See Wang
本文讨论三维正压可压缩NAIVER-STOKES系统在物理上真实的外流条件下的解的长时间行为。结果表明，平面边界层(亚音速和跨音速)与平面稀疏波的叠加在较小的初始扰动下是时间渐近稳定的，只要定常解的量级足够小，而稀疏波的波强可能很大。这是关于高维正压可压缩Navier-Stokes系统在外流边界条件下复合波型稳定性的首次结果。我们的方法是基于非线性能量方法。
In this paper, we are concerned with the long-time behavior of solution to the barotropic compressible Naiver-Stokes system in three dimensions with physically realistic outflow condition. It is shown that the superposition of a planar boundary layer (both subsonic case and transonic case) and a planar rarefaction wave is time asymptotically stable under small initial perturbation, provided that the magnitude of the stationary solution is sufficiently small, while the wave strength of rarefaction wave may be large. This is the first result on the stability of composite wave patterns for the barotropic compressible Navier-Stokes system in high dimensions with outflow boundary condition. Our approach is based on the nonlinear energy methods.