On degenerate circular and shear flows: the point vortex and power law circular flows
On degenerate circular and shear flows: the point vortex and power law circular flows
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关于简并环流和剪切流：点涡流和幂律环流
DOI：
10.1080/03605302.2018.1542436
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发表时间：
2018
影响因子：
1.9
通讯作者：
C. Zillinger
中科院分区：
文献类型：
--
作者：
Michele Coti Zelati;C. Zillinger
摘要本文研究了点涡扰动和类似退化环流的渐近稳定性和线性无粘阻尼问题。在这里，关键的挑战包括缺乏严格的单调性，以及在加权Sobolev空间中工作的必要性，其权重随着半径趋于零或无穷大而退化。通过使用傅立叶乘子的方法，我们构造能量泛函推导出在微扰设置的稳定性。对于足够高的球谐函数，我们可以处理任何具有幂律奇点或零的圆形流动，而对于低频率，我们可以处理接近泰勒-库埃特流动的圆形流动。类似的结果也适用于库埃特附近的平面剪切流情况。
Abstract We consider the problem of asymptotic stability and linear inviscid damping for perturbations of a point vortex and similar degenerate circular flows. Here, key challenges include the lack of strict monotonicity and the necessity of working in weighted Sobolev spaces whose weights degenerate as the radius tends to zero or infinity. By using a Fourier multiplier approach, we construct energy functionals to deduce stability in a perturbative setting. For sufficiently high spherical harmonics, we can handle any circular flows with power law singularities or zeros as or , while for low frequencies we can treat circular flows close to the Taylor–Couette flow. Similar results apply in the planar shear flow case close to Couette.
线性化二维欧拉方程中的涡轴对称化、无粘阻尼和涡耗
影响因子：
2.8
作者：
Bedrossian, Jacob;Coti Zelati, Michele;Vicol, Vlad
通讯作者：
Vicol, Vlad