Real Analytic Local Well‐Posedness for the Triple Deck
Real Analytic Local Well‐Posedness for the Triple Deck
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DOI：
10.1002/cpa.21894
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发表时间：
2019-05
影响因子：
3
通讯作者：
Sameer Iyer;V. Vicol
中科院分区：
文献类型：
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作者：
Sameer Iyer;V. Vicol
三层模型是一种经典的高阶边界层模型，它被用来描述普朗特尔理论可能失效的流动状态。乍一看，该模型似乎通过将压力与切向滑移联系起来的压力-位移关系失去了两个导数。为了克服这一问题，我们将三层系统分解为两个耦合方程：一个在<s:1>上的Prandtl型系统和一个在∈上的Benjamin‐Ono型方程。这种分裂使我们能够在下层甲板的顶部提取一个关键的导阶抵消。我们开发了一个功能框架，随后将这种消去扩展到下层甲板的内部，这使我们能够证明模型在切向实解析空间中的局部适定性。©2019 Wiley期刊公司
The triple‐deck model is a classical high‐order boundary layer model that has been proposed to describe flow regimes where the Prandtl theory is expected to fail. At first sight the model appears to lose two derivatives through the pressure‐displacement relation that links pressure to the tangential slip. In order to overcome this, we split the triple‐deck system into two coupled equations: a Prandtl‐type system on ℍ and a Benjamin‐Ono‐type equation on ℝ. This splitting enables us to extract a crucial leading‐order cancellation at the top of the lower deck. We develop a functional framework to subsequently extend this cancellation into the interior of the lower deck, which enables us to prove the local well‐posedness of the model in tangentially real analytic spaces. © 2019 Wiley Periodicals, Inc.