We study the asymptotic behavior of global classical solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations and kinematic transport equations for the molecular orientations. We prove the convergence of global solutions to single steady states as time tends to infinity as well as estimates on the convergence rate both in 2D for arbitrary regular initial data and in 3D for certain particular cases.
|Original language||English (US)|
|Number of pages||27|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Nov 2012|
All Science Journal Classification (ASJC) codes
- Applied Mathematics