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 long-time 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.
On the long-time behavior of some mathematical models for nematic liquid crystals / H. Petzeltova, E. Rocca, G. Schimperna. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 46:3-4(2013), pp. 623-639. [Epub ahead of print] [10.1007/s00526-012-0496-1]
On the long-time behavior of some mathematical models for nematic liquid crystals
E. RoccaSecondo
;
2013
Abstract
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 long-time 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.File | Dimensione | Formato | |
---|---|---|---|
10.1007s00526-012-0496-1.pdf
Open Access dal 04/03/2013
Tipologia:
Publisher's version/PDF
Dimensione
281.28 kB
Formato
Adobe PDF
|
281.28 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.