题目：Decay Estimates of the Stokes Semigroup for Two-Phase Incompressible Viscous Flows
报告人：Prof. Hirokazu Saito （The University of Electro-Communications）
摘要：In this talk, we consider time decay estimates of Lp-Lq type for the Stokes semigroup arising from study of two-phase incompressible viscous flows. An upper half space like domain is occupied by an incompressible viscous fluid, called the upper fluid, while its complement in the whole space is occupied by another incompressible viscous fluid, called the lower fluid. It is well known that the Rayleigh-Taylor instability occurs due to gravity if the upper fluid is heavier than the lower one. On the other hand, we consider in this talk the following two cases:
(i) the lower fluid is heavier than the upper one;
(ii) the two fluids have equal density.
For these two cases, we introduce decay estimates as mentioned above.