We show that switching in ferroelectric lead germanate and lead iron tantalate zirconate titanate (PZTFT) does not resemble the equilibrium domain structure evolution of the Landau-Lifshitz-Kittel model but is instead highly nonequilibrium and similar, respectively, to the Richtmyer-Meshkov instability in liquids and the Helfrich-Hursault sliding instability in liquid crystals. The resulting nano-domain structures in PZTFT are circular or parabolic and involving folding bifurcations. These may have an undesirable impact on ferroelectric thin-film memoriesthat are also ferroelastic.