Existence, Uniqueness, Regularity and Long-term Behavior for Dissipative Systems Modeling Electrohydrodynamics

We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and for small data in data in three space dimensions. The existence in three dimensions is established by studying a linearization of a relative entropy functional. We also establish the convergence to the stationary solution with a rate

Local Changes in Lipid Composition to Match Membrane Curvature

A continuum mechanical model based on the Helfrich Hamiltonian is devised to investigate the coupling between lipid composition and membrane curvature. Each monolayer in the bilayer is modeled as a freely deformable surface with a director field for lipid orientation. A scalar field for the mole fraction of two lipid types accounts for local changes in composition. It allows lipids to access monolayer regions favorable to their intrinsic curvature at the expense of increasing entropic free energy. Hemifusion is one of the key fusion intermediates with regions of both positive and negative membrane curvature and where proteins must supply energy in order to bring about large elastic distortions. Using a numerical gradient descent scheme, minimal energy axisymmetric shapes of hemifusion diaphragms are calculated for varying radii. Previous studies assumed a fixed, weighted average for spontaneous curvature. Allowing for local changes in spontaneous curvature yields energies and forces of expansion significantly lower than those obtained from a fixed composition