Eigenvalue Constraints and Regularity of

Q-tensor Navier-Stokes Dynamics

October 31, 2013, 15:30-14:30PM,Seminar Room 1219,

Department of Mathematics, Chungnam National University

The Q-tensor is a traceless and symmetric 3 3 matrix that describes the

small-scale structure in nematic liquid crystals. In order to be physically mean-

ingful, its eigenvalues should be bounded below by 1=3 and above by 2=3.

This constraint raises questions regarding the physical predictions of theories

which employ the Q-tensor; it also raises analytical issues in both static and

dynamic Q-tensor theories of nematic liquid crystals. John Ball and Apala Ma-

jumdar recently constructed a singular map on traceless, symmetric matrices

that penalises unphysical Q-tensors by giving them an innite energy cost. In

this talk, I shall present some mathematical results for a coupled Navier-Stokes

system modelling nematic dynamics into which this map is built, including the

existence, regularity and so-called `strict physicality' of its weak solutions.