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Abstract

We discuss the implications of the incompressibility approximation on the number of relevant transport parameters, like viscosities, flow alignment coefficients, and rotational viscosities in uniaxial and biaxial nematic liquid crystals. A comparison between the hydrodynamic and the Leslie-Ericksen approach is given. Agreement is found, if in the latter description a redefinition of the pressure is assumed. For systems with positional order, like smectic and columnar liquid crystals and crystals, we show that, generally, incompressibility does not imply that the displacement field is source-free.