多维非特征粘性边界层的长时间稳定性
Long-time stability of multi-dimensional noncharacteristic viscous boundary layers
摘要：
在强谱稳定性或一致Evans稳定性的假设下，我们建立了一类双曲抛物方程组的多维非特征边界层的长时间稳定性，该方程组包括具有流入[流出]边界条件的可压缩纳维-斯托克斯方程。埃文斯稳定性已经被Guès、Métivier、Williams和Zumbrun验证过。对于大振幅层，可以有效地进行数值检验，如Costanzino、Humpherys、Nguyen和Zumbrun在一维情况下所做的那样。
英文摘要：
We establish long-time stability of multi-dimensional noncharacteristic boundary layers of a class of hyperbolic--parabolic systems including the compressible Navier--Stokes equations with inflow [outflow] boundary conditions, under the assumption of strong spectral, or uniform Evans, stability. Evans stabiity has been verified for small-amplitude layers by Guès, Métivier, Williams, and Zumbrun. For large-amplitude layers, it may be efficiently checked numerically, as done in the one-dimensional case by Costanzino, Humpherys, Nguyen, and Zumbrun.
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