Abstract In this paper we consider the 2D Ericksen–Leslie equations which describe hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling applied control such as magnetic or electric field. Under general assumptions on initial data, data energy, prove existence uniqueness global weak solutions finitely many singular times. If are sufficiently small, th...

We investigate existence and regularity of weak solutions a 1-dimensional parabolic differential equation with non-constant Hölder diffusion coefficient rough forcing term. Such an appears in studying the Ericksen-Leslie model for nematic liquid crystals where our result applies. The presented here uses continuity which comes from physical background analysis model. Moreover, dependence exponen...

We consider here the simplified Ericksen–Leslie system on whole space $$\mathbb {R}^{3}$$ . This deals with incompressible Navier–Stokes equations strongly coupled a harmonic map flow which models dynamical behavior for nematic liquid crystals. For both, stationary (time independent) case and non-stationary dependent) case, using fairly general framework of kind local Morrey spaces, we obtain s...