[en] We examine some leading-order flow and stability properties of smectic A (SmA) liquid crystals (LCs) in two spatial dimensions by analysing a fully nonlinear continuum theory of these materials. We derive a system of equations for the dynamic variables describing the flow velocity and orientation of the material under suitable assumptions upon these quantities. This system can provide insight into the leading-order behaviour under quite general circumstances, and we provide an example of utilising this system to determine the flow induced by a constant pressure gradient applied normally to the smectic layers. We then consider the effect of oscillatory perturbations on a relaxed, stationary sample of SmA, and provide criteria under which one would expect to see the onset of instability in the form of inequalities between the material parameters and perturbative wave number. We find that instability occurs for physically realisable values of these quantities, and, in particular, that certain viscosities characterising the SmA phase can act as ‘destabilising agents’ such that one could, for a given sample with known parameter values, manipulate the behaviour of that sample. (paper)

[en] We discuss the static configuration of a smectic A liquid crystal subject to an edge dislocation under the assumption that the director and layer normal fields ($\mathit{n}$ and $\mathit{a}$, respectively) defining the smectic arrangement are not, in general, equivalent. After constructing the free energy for the smectic, we obtain exact solutions to the equilibrium equations which result from its minimisation at quadratic order in the variables which describe the distortion, and hence a complete description of the smectic configuration across the domain of the sample. We also examine the effect of relaxing the constraint $\mathit{n}\equiv <!--\; ???\; -->\mathit{a}$ for different values of the constants which characterise the response of the material to distortions, and compare these results with the ‘classical’ case considered by previous authors, in which equivalence of $\mathit{n}$ and $\mathit{a}$ is enforced. (paper)