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PDE Real Analysis Seminar
Seminar information archive ～04/22｜Next seminar｜Future seminars 04/23～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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2013/07/23
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Matthias Hieber (Technische Universität Darmstadt)
Analysis of the Simplified Ericksen-Leslie Model for Liquid Crystals (ENGLISH)
Matthias Hieber (Technische Universität Darmstadt)
Analysis of the Simplified Ericksen-Leslie Model for Liquid Crystals (ENGLISH)
[ Abstract ]
Consider the Ericksen-Leslie model for the flow of liquid crystals in a bounded domain $\\Omega \\subset \\R^n$. In this talk we discuss various simplifications of the general model and describe a dynamic theory for the simplified equations by analyzing it as a quasilinear system. In particular, we show the existence of a unique, global, strong solutions to this system provided the initial data are close to an equilibrium or the solution is eventually bounded in the norm of the underlying state space. In this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.
We further analyze a non-isothermal extension of this model safisfying the first and second law of thermodynamics and show that results of the above type hold as well in this setting.
This is joint work with M. Nesensohn, J. Prüss and K. Schade.
Consider the Ericksen-Leslie model for the flow of liquid crystals in a bounded domain $\\Omega \\subset \\R^n$. In this talk we discuss various simplifications of the general model and describe a dynamic theory for the simplified equations by analyzing it as a quasilinear system. In particular, we show the existence of a unique, global, strong solutions to this system provided the initial data are close to an equilibrium or the solution is eventually bounded in the norm of the underlying state space. In this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.
We further analyze a non-isothermal extension of this model safisfying the first and second law of thermodynamics and show that results of the above type hold as well in this setting.
This is joint work with M. Nesensohn, J. Prüss and K. Schade.
