In this paper, we prove the existence of global-in-time weak solutions for an evolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible Navier-Stokes system for the macroscopic velocity is coupled to a nonlinear convective parabolic equation describing the evolution of the Q-tensor Q, namely a tensor-valued variable representing the normalized second-order moments of the probability distribution function of the LC molecules. The effects of the (absolute) temperature are prescribed in the form of an energy balance identity complemented with a global entropy production inequality. Compared to previous contributions, we can consider here the physically realistic singular configuration potential introduced by Ball and Majumdar. This potential gives rise to severe mathematical difficulties since it introduces, in the Q-tensor equation, a term that is at the same time singular in Q and degenerate in v. To treat it, a careful analysis of the properties of , particularly of its blow-up rate, is carried out.

Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy / E. Feireisl, E. Rocca, G. Schimperna, A. Zarnescu. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 194:5(2015 Oct), pp. 1269-1299. [10.1007/s10231-014-0419-1]

Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy

E. Rocca;
2015

Abstract

In this paper, we prove the existence of global-in-time weak solutions for an evolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible Navier-Stokes system for the macroscopic velocity is coupled to a nonlinear convective parabolic equation describing the evolution of the Q-tensor Q, namely a tensor-valued variable representing the normalized second-order moments of the probability distribution function of the LC molecules. The effects of the (absolute) temperature are prescribed in the form of an energy balance identity complemented with a global entropy production inequality. Compared to previous contributions, we can consider here the physically realistic singular configuration potential introduced by Ball and Majumdar. This potential gives rise to severe mathematical difficulties since it introduces, in the Q-tensor equation, a term that is at the same time singular in Q and degenerate in v. To treat it, a careful analysis of the properties of , particularly of its blow-up rate, is carried out.
nematic liquid crystal; Ball-Majumdar free energy; nonisothermal model; existence theorem
Settore MAT/05 - Analisi Matematica
ott-2015
21-apr-2014
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/345077
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