标题： 一种剪切流线性不稳定的简单证明及其在涡旋片中的应用 显示英文标题

标题： A simple proof of linear instability of shear flows with application to vortex sheets

摘要： 我们考虑平行剪切流线性不稳定的构造，这是由林志武（SIAM J. Math. Anal. 35(2), 2003）发展的。我们给出了该问题在Sobolev框架下的另一种简单的证明，揭示了Plemenj-Sokhotski公式在不稳定性的出现中的作用，同时不需要锥条件。此外，我们将这种方法局部化，以获得平坦涡量片的Kelvin-Helmholtz不稳定的近似。 显示英文摘要

摘要： We consider the construction of linear instability of parallel shear flows, which was developed by Zhiwu Lin (SIAM J. Math. Anal. 35(2), 2003). We give an alternative simple proof in Sobolev setting of the problem, which exposes the role of the Plemenj-Sokhotski formula in the emergence of the instability, as well as does not require the cone condition. Moreover, we localize this approach to obtain an approximation of the Kelvin-Helmholtz instability of a flat vortex sheet.