偏微分方程系列报告

报告题目: Rayleigh--Taylor Instability in Stratified Compressible Fluids with/without the Interfacial Surface Tension

报告人:  江飞 教授 （福州大学 数学与计算机科学学院）

报告摘要： Guo--Tice formally  established in 2011 that the linear Rayleigh--Taylor instability inevitably occurs within stratified compressible viscous fluids in a slab domain $\mathbb{R}^2\times (h_-,h_+)$, irrespecive of the presence of interfacial surface tension, where the instability solutions are non-periodic with respect to both horizontal spacial variables $x_1$ and $x_2$, by applying a so-called ``normal mode'' method and a modified variational method to the linearized (motion) equations. It remains an open problem, however, whether Guo--Tice's conclusion can be rigorously verified by the (original) nonlinear equations. This challenge arises due to the failure of constructing a growing mode solution, which is non-periodic with respect to both horizontal spacial variables, to the linearized equations defined on a slab domain. In the present work, we circumvent the difficulty related to growing mode solutions by developing an alternative approximate approach. In essence, our approach hinges on constructing the horizontally periodic growing mode solution of the linearized equations to approximate the nonlinear Rayleigh--Taylor unstable solutions, which do not exhibit horizontal periodicity. Thanks to this new approximate approach, we can apply Guo--Hallstrom--Spirn's bootstrap instability method to the nonlinear equations in Lagrangian coordinates, and thus prove Guo--Tice's conclusion. In particular, our approximate approach could also be applied to other unstable solutions characterized by non-periodic motion in a slab domain, such as the Parker instability and thermal instability.

报告人简介：江飞，教授，博士生导师，主要研究领域为流体动力学中各类偏微分方程组的适定性问题及解的性态，已在《Arch. Rational Mech. Anal.》、《Adv. Math.》、《Comm. Partial Differential Equations》、《J. Funct. Anal.》、《SIAM J. Math. Anal.》、《J. Math. Pures Appl.》、《J Differ. Equations》、《J. Math. Fluid Mech.》、《SIAM J. App. Math.》等SCI学术期刊发表论文40余篇。主持多项国家自然科学基金项目。

报告时间：2023.11.02  下午4:00-5：30

报告地点：腾讯会议 ID：476 248 126，密码：1102