PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Becky Halpenny.

Title:"Topics on Stability of Complex Fluid Models"
Seminar:Ph.D. Thesis Defense
Speaker:Xiang Xu, Adviser: Chun Liu, Penn State
Abstract:
In this thesis, we study analytical problems related to two models in the hydrodynamics of complex fluids. The first is the general Ericksen-Leslie system, which models nematic liquid crystal flow, while the latter is a diffuse-interface model for the mixture of two incompressible fluids. Both models are based on a special coupling between the induced elastic stress and transport property of microstructures. Both models can be derived in the energetic variational framework which demonstrates the consistent exchange of the kinetic energy of the fluid and internal energy due to elastic effects. For the general Ericksen-Leslie system, in both the two and three dimensional cases, we develop the existence theory for global classical solutions with various assumptions on physical relations between viscosity coefficients. Meanwhile, we study the asymptotic behavior of global bounded solutions as time goes to infinity and show that the asymptotic limit is unique. More importantly, we reveal the various roles of physical relations on corresponding analytical results. For the diffuse-interface model, within the study of axisymmetric solutions, we construct perturbations to near infinite-energy solutions.

Room Reservation Information

Room Number:MB106
Date:04 / 19 / 2011
Time:08:00am - 09:44am