AI 中文总结
本文研究一维纳维-斯托克斯-傅里叶系统半直线流入问题解的时间渐近稳定性，采用带平移的a-收缩方法，解决了含大强度稀疏波的粘性激波流入波型稳定性的开放问题。
AI 中文摘要
我们研究一维纳维-斯托克斯-傅里叶系统在半直线上的流入问题解的时间渐近稳定性。我们考虑最通用的波型：退化边界层、稀疏波、粘性接触波与粘性激波的叠加。更确切地说，若边界数据属于亚声速区域，且初始扰动、边界层、粘性接触波及粘性激波的强度均足够小，则流入问题的解会收敛到对应的叠加态（激波存在随时间变化的平移）。但稀疏波的强度可任意大。为控制粘性激波，我们采用带平移的a-收缩方法。本分析的一个显著特点是，该方法即使在稀疏波振幅很大时也能应用。特别地，这在通用情形下解决了纳维-斯托克斯-傅里叶系统含粘性激波的流入波型稳定性这一开放问题。
英文摘要
We study the time-asymptotic stability of solutions to the inflow problem for the one-dimensional Navier--Stokes--Fourier system on the half-line. We consider the most generic wave pattern: the superposition of a degenerate boundary layer, a rarefaction, a viscous contact wave, and a viscous shock. More precisely, if the boundary data belongs to the subsonic region, and the initial perturbation and strengths of the boundary layer, viscous contact wave, and viscous shock are sufficiently small, then the solution to the inflow problem converges to the corresponding superposition, up to a time-dependent shift for a shock. The rarefaction wave, however, is allowed to have arbitrarily large strength. To control the viscous shock, we employ the method of $a$-contraction with shifts. A notable feature of our analysis is that this method can be applied even when the rarefaction wave has large amplitude. In particular, this resolves, in a generic setting, the open problem of the stability of inflow wave patterns containing a viscous shock for Navier--Stokes--Fourier system.
