报告题目：The Viscous Surface-Internal Wave Problem: Nonlinear Rayleigh–Taylor Instability

报告人：厦门大学王焰金（教授）

报告时间：12月20日上午8:00-8:45

报告地点：数计学院4号楼302室

We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh–Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.

报告题目：The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay

报告人：厦门大学王焰金（教授）

报告时间：12月20日上午10:00-10:45

报告地点：数计学院4号楼302室

We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the global well-posedness of the problem both with and without surface tension. We prove that without surface tension the solution decays to the equilibrium state at an almost exponential rate; with surface tension, we show that the solution decays at an exponential rate. Our results include the case in which a heavier fluid lies above a lighter one, provided that the surface tension at the free internal interface is above a critical value, which we identify. This means that sufficiently large surface tension stabilizes the Rayleigh–Taylor instability in the nonlinear setting. As a part of our analysis, we establish elliptic estimates for the two-phase stationary Stokes problem.

王焰金教授：1984年生，主要从事流体力学中的非线性偏微分方程的数学理论研究。2013年获全国百篇优秀博士学位论文奖；2015年获福建省自然科学杰出青年基金及高校新世纪优秀人才支持计划资助。在Archive for Rational Mechanics and Analysis，Communications in Mathematical Physics，SIAM Journal on Mathematical Analysis，Communications in Partial Differential Equations，Annales de l'Institut Henri PoincaréAnalyse non linéaire，Journal of Differential Equations等高水平杂志上发表数十篇数学研究论文。 

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