Stability of equilibrium figures of a rotating capillary two-layer incompressible fluid

Speaker: Prof. Denisova Irina Vlad，Institute for Problems in Mechanical Engineering , Russian Academy of Sciences            

Inviter: 郝成春

Title: Stability of equilibrium figures of a rotating capillary two-layer incompressible fluid

Language: English

Time & Venue: 2026.05.27  14:00-16:00  南楼N913

Abstract: A uniformly rotating finite mass consisting of two immiscible viscous fluids is studied. This motion is described by a problem with unknown boundaries for the Navier-Stokes system. The interface between the fluids is assumed to be closed. Surface tension acts on both the interface and the outer free surface. The stability of a rotating two-layer drop with self-gravity is proved for sufficiently small initial data, angular velocity, and exponentially decreasing mass forces, as well as for the positivity of the second variation of the energy functional. The proof is based on an analysis of small perturbations of the equilibrium state of a rotating two-layer fluid.Furthermore, the existence of equilibrium figures is proven in the two-layer case when one (or both) of the fluids is compressible. If the pressure function is defined by a smooth, increasing density function for a compressible fluid, and the problem data satisfy a certain condition, then for a two-phase (two-layer compressible) fluid with low angular momentum, axisymmetric equilibrium figures similar to nested spheres exist.