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

0446507 - MÚ 2017 RIV DE eng J - Journal Article
Feireisl, Eduard - Schimperna, G. - Rocca, E. - Zarnescu, A.
Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy.
Annali di Matematica Pura ed Applicata. Roč. 194, č. 5 (2015), s. 1269-1299. ISSN 0373-3114. E-ISSN 1618-1891
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : nematic liquid crystal * Ball-Majumdar free theory * nonisothermal model * existence theorem
Subject RIV: BA - General Mathematics
Impact factor: 0.861, year: 2015
http://link.springer.com/article/10.1007%2Fs10231-014-0419-1

In this paper, we prove the existence of global-in-time weak solutions for an evolutionary PDE systemmodelling 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 u 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 ϑ 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 f introduced by Ball and Majumdar.
Permanent Link: http://hdl.handle.net/11104/0248487