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On a Boundary Layer in Nematodynamics
时间  Datetime
2017-05-08 16:00 — 17:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
Maxim S. Romanov
单位  Affiliation
Lomonosov Moscow State University
邀请人  Host
Tudor Stefan Ratiu
报告摘要  Abstract

The talk will be devoted to the Ericksen-Leslie model of nematic liquid crystals. Liquid crystal is a non-homogeneous media, consisting of the viscous liquid with dispersed relatively big molecules of dissolved substance. In the case of nematic liquid crystal the molecules are axially symmetric, e.g. they are discoid or rode-like. Orientation of the molecule can be described with a unit director vector collinear to the axis of symmetry of the molecule. In general case the Ericksen-Leslie system is quite complex. Any known existence theorem in the case of non-zero inertial constant guarantees only the existence of the short-time solution. In the talk we consider two-dimentional axisymmetric Ericksen-Leslie equations with the non-zero inertial constant. In this case the existence of the global-time solution was proved. Under the assumption that Reynolds number is large enough we derive the boundary layer equations, describing the motion of the media in the neighbourhood of the solid surface. The solution of the new problem is close to the solution of the original one. The error estimates are obtained. Also we show that the effective viscosity of the fluid in the boundary layer decreases as the inertial constant grows.