  If a surface stabilized ferroelectric liquid crystal cell is cooled from the
smectic-A to the smectic-C phase, its layers thin causing V-shaped (chevron
like) defects to form. These create an energy barrier that can prevent
switching between equilibrium patterns. We examine a gradient flow for a
mesoscopic Chen-Lubensky energy $\mathcal{F}(\psi,\mathbf{n})$ that allows the
order parameter to vanish, so that the energy barrier does not diverge if the
layer thickness becomes small. The liquid crystal can evolve during switching
in such a way that the layers are allowed to melt and heal near the chevron tip
in the process.
