The Ericksen model for nematic liquid crystals couples a director field with scalar degree of orientation variable and allows the formation various defects finite energy. We propose simple but novel element approximation problem that can be implemented easily within standard packages. Our scheme is projection-free thus circumvents use weakly acute meshes, which are quite restrictive in three di...

In this article, we consider the Ericksen-Leslie's hyperbolic system for compressible liquid crystal model in three spatial dimensions. Global regularity small and smooth initial data near equilibrium is proved case that a nonlinear coupling of Navier-Stokes equations with wave map to $\mathbb{S}^2$. Our argument combination vector field method Fourier analysis. The main strategy prove global r...

The hydromagnetic instability of the plane interface between two uniform, superposed and streaming Rivlin-Ericksen viscoelastic fluids through porous medium is considered. The case of two uniform streaming fluids separated by a horizontal boundary is studied. It is observed, for the special case where perturbations in the direction and transverse direction of streaming are ignored, that the sys...

The previous energetic variational analysis of critical loads and of the choice of finite strain measure for structures very weak in shear, remaining in a state of small strain, is extended to the initial postcritical behavior. For this purpose, consideration of the transverse deformation is found to be essential. It is shown that imperfection sensitivity of such structures, particularly lamina...