Dynamics of the Ericksen-Leslie Equations with General Leslie Stress I: The Incompressible Isotropic Case

The Ericksen-Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally well-posed in the $L_p$-setting, and a dynamic theory is developed. The equilibria are identified and shown to be normally stable. In particular, a local solution extends to a unique, global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the topology of the natural state manifold. In this case, the solution converges exponentially to an equilibrium, in the topology of the state manifold. The above results are proven {\em without} any structural assumptions on the Leslie coefficients and in particular {\em without} assuming Parodi's relation

The trade-off between scope and precision in sustainability assessments of food systems

With sustainability becoming an increasingly important issue, several tools have been developed, promising to assess sustainability of farms and farming systems. However, looking closer at the scope, the level of assessment and the precision of indicators used for impact assessment we discern considerable differences between the sustainability impact assessment tools at hand. The aim of this paper is therefore to classify and analyse six different sustainability impact assessment tools with respect to the assessment level, the scope and the precision. From our analysis we can conclude that there is a trade-off between scope and precision of these tools. Thus one-size-fits-all solutions with respect to tool selection are rarely feasible. Furthermore, as the indicator selection determines the assessment results, different and inconsistent indicators could lead to contradicting and not comparable assessment results. To overcome this shortcoming, sustainability impact assessments should disclose the methodological approach as well as the indictor sets use and aim for harmonisation of assumptions

On a Class of Energy Preserving Boundary Conditions for Incompressible Newtonian Flows

We derive a class of energy preserving boundary conditions for incompressible Newtonian flows and prove local-in-time well-posedness of the resulting initial boundary value problems, i.e. the Navier-Stokes equations complemented by one of the derived boundary conditions, in an Lp-setting in domains, which are either bounded or unbounded with almost flat, sufficiently smooth boundary. The results are based on maximal regularity properties of the underlying linearisations, which are also established in the above setting.Comment: 53 page