caa a22 4500 605496560 CHVBK 20210128100537.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10231-014-0419-1 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0419-1 Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy [Elektronische Daten] [Eduard Feireisl, Giulio Schimperna, Elisabetta Rocca, Arghir Zarnescu] 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 $$\mathbf{u}$$ u is coupled to a nonlinear convective parabolic equation describing the evolution of the $$Q$$ Q -tensor $$\mathbb {Q}$$ 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 $$\vartheta $$ 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 $$f$$ f introduced by Ball and Majumdar. This potential gives rise to severe mathematical difficulties since it introduces, in the $$Q$$ Q -tensor equation, a term that is at the same time singular in $$\mathbb {Q}$$ Q and degenerate in $$\vartheta $$ ϑ . To treat it, a careful analysis of the properties of $$f$$ f , particularly of its blow-up rate, is carried out. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Nematic liquid crystal nationallicence Ball-Majumdar free energy nationallicence Nonisothermal model nationallicence Existence theorem nationallicence Feireisl Eduard Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567, Praha 1, Czech Republic aut Schimperna Giulio Dipartimento di Matematica, Università di Pavia, Via Ferrata1, 27100, Pavia, Italy aut Rocca Elisabetta Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr.39, 10117, Berlin, Germany aut Zarnescu Arghir Pevensey III, University of Sussex, BN1 9QH, Falmer, UK aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1269-1299 0373-3114 194:5<1269 2015 194 10231 https://doi.org/10.1007/s10231-014-0419-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0419-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Feireisl Eduard Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567, Praha 1, Czech Republic aut NATIONALLICENCE 700 1- Schimperna Giulio Dipartimento di Matematica, Università di Pavia, Via Ferrata1, 27100, Pavia, Italy aut NATIONALLICENCE 700 1- Rocca Elisabetta Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr.39, 10117, Berlin, Germany aut NATIONALLICENCE 700 1- Zarnescu Arghir Pevensey III, University of Sussex, BN1 9QH, Falmer, UK aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1269-1299 0373-3114 194:5<1269 2015 194 10231