Asymptotic Stability for the Couette Flow in the 2D Euler Equations
Asymptotic Stability for the Couette Flow in the 2D Euler Equations
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DOI：
10.1093/amrx/abt009
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发表时间：
2014-01-01
期刊：
影响因子：
--
通讯作者：
Masmoudi, Nader
中科院分区：
文献类型：
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作者：
Bedrossian, Jacob;Masmoudi, Nader
在这篇说明性说明中，我们讨论了我们最近关于理想不可压缩流的二维欧拉方程中剪切流的非线性渐近稳定性的工作 [7]。在那项工作中，证明了在适当的规则类中对库埃特流的扰动很小，在 L-2 中强烈收敛到接近库埃特流的剪切流。熵通过几乎线性的演化混合到小尺度，并且通常在 t ->+/-无穷大的弱极限中丢失。在这篇笔记中，我们讨论了结果中最重要的物理和数学方面以及证明的关键思想。
In this expository note, we discuss our recent work [7] on the nonlinear asymptotic stability of shear flows in the 2D Euler equations of ideal, incompressible flow. In that work, it is proved that perturbations to the Couette flow which are small in a suitable regularity class converge strongly in L-2 to a shear flow which is close to the Couette flow. Enstrophy is mixed to small scales by an almost linear evolution and is generally lost in the weak limit as t ->+/-infinity. In this note, we discuss the most important physical and mathematical aspects of the result and the key ideas of the proof.