Corrigendum to “Stationary inviscid limit to shear flows” [J. Differ. Equ. 267 (12) (2019) 7135–7153]
Corrigendum to “Stationary inviscid limit to shear flows” [J. Differ. Equ. 267 (12) (2019) 7135–7153]
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对“剪切流的稳态无粘极限”的勘误 [J.
DOI：
10.1016/j.jde.2021.04.015
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发表时间：
2021
影响因子：
2.4
通讯作者：
Zhou, Chunhui
中科院分区：
文献类型：
--
作者：
Iyer, Sameer;Zhou, Chunhui
这个错误是为了纠正我们的原始文章附录中的一个错误，“剪切流的静止无粘极限”。具体地说，我们在(65)-(66)中构造我们的(ε中的高阶)“边界层”项[U1p，v1p]和[U2p，v2p]的方法需要修改。我们将首先解释，然后严格确立的修改，对证明的主体没有影响，因为它实际上使这些“边界层条件”变得更弱。结论是，主要定理，即定理1，如原文所述，经修改后，将展开/近似解视为本Erratum的(3)-(5)，而不是原始手稿方程式(6)中所写的解。让我们从描述量u1 p开始。回忆一下从原始论文的(99)开始，我们首先构造u1，0，±p，然后将其截断以形成u1 p。这样我们就集中于量u1，0，−p，它满足以下方程：μ∂xu1，0，−p−∂2 Y−u1，0，−p=0，(x，Y−)∈(0，L)×(0，∞).(1)
This erratum is meant to correct a mistake in the Appendix of our original article,“Stationary inviscid limit to shear flows”. Specifically, the way in which we have constructed our (high order in ε)“boundary layer” terms,[u1 p, v1 p], and [u2 p, v2 p] in (65)-(66) of that paper needs to be modified. The modification, which we shall first explain, then establish rigorously, has no bearing on the body of the proof since it makes these “boundary layer terms” weaker in fact. The conclusion is that the main theorem, Theorem 1, holds as stated in the original paper, with the modification that the expansion/approximate solution is taken to be (3)-(5) of the present Erratum, as opposed to the one written in equation (6) of the original manuscript. Let us start by describing the quantity u1 p. Recall from (99) of the original paper that we first construct u 1, 0,±p, then cut it off to form u1 p. We focus thus on the quantity u 1, 0,− p, which satisfies the following equation: μ∂ xu1, 0,− p−∂ 2 Y− u1, 0,− p= 0,(x, Y−)∈(0, L)×(0,∞).(1)