2 results
Search Results
Now showing 1 - 2 of 2
- ItemAsymptotic behavior of a hydrodynamic system in the nematic liquid crystal flows(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Liu, Chun; Wu, Hao; Xu, XiangIn this paper we study the long time behavior of the classical solutions to a hydrodynamical system modeling the flow of nematic liquid crystals. This system consists of a coupled system of Navier--Stokes equations and kinematic transport equations for the molecular orientations. By using a suitable Lojasiewicz--Simon type inequality, we prove the convergence of global solutions to single steady states as time tends to infinity. Moreover, we provide estimates for the convergence rate.
- ItemA note on a parabolic equation with nonlinear dynamical boundary condition(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Sprekels, Jürgen; Wu, HaoWe consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-called Wentzell boundary condition. First, we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we derive a suitable Lojasiewicz-Simon type inequality to show the convergence of global solutions to single steady states as time tends to infinity under the assumption that the nonlinear terms f, g are real analytic. Moreover, we provide an estimate for the convergence rate.