On the long-time behavior of some mathematical models for nematic liquid crystals

0374133 - MÚ 2013 RIV DE eng J - Journal Article
Petzeltová, Hana - Rocca, E. - Schimperna, G.
On the long-time behavior of some mathematical models for nematic liquid crystals.
Calculus of Variations and Partial Differential Equations. Roč. 46, 3-4 (2013), s. 623-639. ISSN 0944-2669. E-ISSN 1432-0835
R&D Projects: GA MŠMT LC06052
Institutional research plan: CEZ:AV0Z10190503
Keywords : nematic liquid crystals * long-time behavior * flows
Subject RIV: BA - General Mathematics
Impact factor: 1.526, year: 2013
http://www.springerlink.com/content/d61u566014515884/

A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of two basic state variables: the velocity field u and the director field d, representing the preferred orientation of molecules in a neighborhood of any point in a reference domain. After recalling a known existence result, we investigate the longtime behavior of weak solutions. In particular, we show that any solution trajectory admits a non-empty ω-limit set containing only stationary solutions. Moreover, we give a number of sufficient conditions in order that the ω-limit set contains a single point. Our approach improves and generalizes existing results on the same problem.
Permanent Link: http://hdl.handle.net/11104/0207123