On an incompressible non-inertial nematic electrolyte model

This work concerns the incompressible non-inertial electrokinetics model, which consists of various ions species and describes the hydrodynamics of nematic liquid crystals without inertial effect in the Q-tensor framework. This new model was proposed by Tovkach et al. [Phys. Rev. Fluids 2, 053302 (2017)]. We first prove the local well-posedness with large initial data, when the flow is isotropy, i.e., λ = 1. For the anisotropy case (λ > 0, λ ≠ 1), one obtain small data local solutions in the whole space. Furthermore, the global existence near a constant state with small size of the initial data with the electro-neutrality condition is rigorously justified.