主标题：微分方程理论、计算与应用讨论班（4）

报告题目: On Instability in Gravity Driven Viscoelastic Fluid

报告人：中国科学院数学与系统科学研究院  吴国春（博士后）

报告时间：9月30 下午14:30

报告地点：数计学院4号楼229会议室

摘要: In this topic, we investigate the instability of a smooth Rayleigh-Taylor steady-state solution to nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain $\\Omega$ of class $C_2$. We show that the steady-state is linearly unstable by constructing a suitable energy functional and exploiting arguments of the modified variational method. Compared to the Newtonian fluid, the steady-state may be linearly unstable even though the steady density is lighter with increasing height, which means the elasticity can have linearly destabilizing effect. When the derivative of steady density is a nonzero constant, by introducing a new energy function and using a careful bootstrap argument, we further show that the steady-state is nonlinear unstable in the sense of Hadamard.

报告题目: On Stabilizing Effect of Elasticity in Rayleigh-Taylor Problem Arising in Viscoelastic Fluid

报告人：中国科学院数学与系统科学研究院 吴国春（博士后）

报告时间：9月30 下午16:00

报告地点：数计学院4号楼229会议室

摘要: In this topic, we investigate the stability of a smooth Rayleigh-Taylor steady-state solution to nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain $\\Omega$ of class $C_2$.  With the help of a restricted condition imposed on steady density and the speed of propagation of shear waves, we show that the steady-state is linearly globally stable and nonlinearly locally stable in the sense of Hadamard. Compared to the Newtonian fluid, the steady-state may be linearly and nonlinearly stable even though the steady density is heavier with increasing height, which means the elasticity can have stabilizing effect.