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Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics

Monday 8th April 2013 - 15:30 to 16:00
If the Q-tensor order parameter is interpreted as a normalised matrix of second moments of a probability measure on the unit sphere, its eigenvalues are 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 Majumdar recently constructed a singular map on traceless, symmetric matrices that penalises unphysical Q-tensors by giving them an infinite energy cost. In this talk, I shall discuss some mathematical results for a modified Beris-Edwards model of nematic dynamics into which this map is built, including the existence, regularity and so-called `strict physicality' of its weak solutions.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons