标题： 层流剪切流线性不稳定的简单证明及其对涡层的应用 显示英文标题

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

摘要： 我们研究了平行剪切流的线性不稳定性构造，这是由Zhiwu Lin（SIAM J. Math. Anal. 35(2), 2003）发展起来的。我们在Sobolev框架下给出了该问题的一个替代简单证明，这一证明揭示了Plemelj-Sochocki公式在不稳定性出现中的数学作用，并且不需要锥条件。此外，我们将这种方法局部化，以得到平面涡层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 mathematical role of the Plemelj-Sochocki 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.