PDE Real Analysis Seminar
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Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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2013/11/13
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Mark Wilkinson (École normale supérieure - Paris)
Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics (ENGLISH)
Mark Wilkinson (École normale supérieure - Paris)
Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics (ENGLISH)
[ Abstract ]
The Q-tensor is a traceless and symmetric 3x3 matrix that describes the small-scale structure in nematic liquid crystals. In order to be physically meaningful, 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 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 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.
The Q-tensor is a traceless and symmetric 3x3 matrix that describes the small-scale structure in nematic liquid crystals. In order to be physically meaningful, 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 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 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.