On a compressible non-isothermal model for nematic liquid crystals
نویسندگان
چکیده
where the functions ρ, u, θ and d represent the mass density,the velocity field, the absolute temperature and the unit vector field that represents the macroscopic molecular orientation of the liquid crystal material. P stands for the pressure, S denotes the viscous stress tensor. The positive constants ν, κ denote the competition between kinetic energy and potential energy, and microscopic elastic relation time for the molecular orientation field, respectively. ∇d ⊙ ∇d denotes the 3 × 3 matrix whose ijth entry is < ∂xid, ∂xjd >. The vector-valued smooth function f(d) denotes the penalty function and has the following form:
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