We derive the small thickness limit of a three-dimensional model for the ferroelectric polar Smectic A (SmAP) phase found in bent-core liquid crystals (BCLC), and consider its numerical approximation via gradient flow. Time permitting, we will also present numerical and analytical results for a model illustrating topological ferroelectric bistability in the modulated SmAP phase of BCLC. Both models are characterized by the appearance of boundary singularities. This is joint work with C. J. Garcia-Cervera and S. Joo.