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Abstract

Pierre-Gilles de Gennes was awarded the Nobel prize in physics in 1991 for the Landau-de Gennes theory, which generalizes the well-known Oseen-Frank theory. The Ericksen-Leslie system is obtained by coupling the Navier-Stokes equations with the gradient flow for the Oseen-Frank energy.  Based on the celebrated Landau-de Gennes Q-tensor theory, Beris-Edwards proposed a hydrodynamic theory to generalize the Ericksen-Leslie system from uniaxial to biaxial nematic liquid crystals. In this talk, we will give a general introduction to the Ericksen-Leslie system and the Beris-Edwards system. We will discuss some new mathematical results.