Abelian--Higgs--Navier--Stokes Hydrodynamics for Nematic Films with Defects

A new theory of hydrodynamics of uniaxial nematic liquid crystal films in the presence of defects is developed. A gauge field incorporating screening is introduced, resulting in the static elastic free energy having the form of a two-dimensional Abelian-Higgs model. Hydrodynamic equations are derived via the standard methods of de~Groot and Mazur. By working in the vicinity of the Bogomol'nyi equations consequences for defect centre motion are outlined.