Sobolev Stability of Prandtl Expansions for the Steady Navier–Stokes Equations
Sobolev Stability of Prandtl Expansions for the Steady Navier–Stokes Equations
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DOI：
10.1007/s00205-019-01380-x
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发表时间：
2019-04
影响因子：
2.5
通讯作者：
D. Gérard-Varet;Yasunori Maekawa
中科院分区：
文献类型：
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作者：
D. Gérard-Varet;Yasunori Maekawa
本文在二维定常Navier-Stokes方程中，在自然假设下，证明了Prandtl型剪切流的H_1稳定性。我们的结果是在形成鲜明对比的非定常的，其中最多Gevrey稳定性可以得到，即使在全局单调性和非线性假设。这提供了第一个肯定的答案，无粘极限问题的Sobolev正则性的非平凡类的稳定的Navier-Stokes流与无滑移边界条件。
We show theH1stability of shear flows of Prandtl type:, in the steady two-dimensional Navier–Stokes equations, under the natural assumptions thatfor,, and. Our result is in sharp contrast with the unsteady ones, in which at most Gevrey stability can be obtained, even under global monotonicity and concavity hypotheses. This provides the first positive answer to the inviscid limit problem in Sobolev regularity for a non-trivial class of steady Navier–Stokes flows with no-slip boundary condition.