报告人：陈明(匹兹堡大学)

时间：2022年10月20日 9:00-

腾讯会议ID：220 358 991

摘要：I will discuss the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regions is governed by the incompressible and irrotational Euler equations, with the density of each fluid being constant but distinct. We prove that for supercritical surface tension, all known small-amplitude localized waves are (conditionally) orbitally stable in the natural energy space. Moreover, the trivial solution is shown to be conditionally stable when the Bond and Froude numbers lie in a certain unbounded parameter region. For the near critical surface tension regime, we show that one can infer conditional orbital stability or orbital instability of small-amplitude traveling waves solutions to the full Euler system from considerations of a dispersive PDE similar to the steady Kawahara equation. This is joint work with S. Walsh.

简介：陈明，美国匹兹堡大学数学系教授，博士毕业于美国布朗大学，师从国际著名数学家Walter Strauss教授。主要从事偏微分方程的稳定性理论及非线性波等问题的研究，已在 Adv. Math.、Trans. Amer. Math. Soc.、Comm. Math. Phys.、Arch. Ration. Mech. Anal.、Indiana U. J. Math等杂志上发表论文30余篇。

邀请人：穆春来       王华桥

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