Energy Equality, Vectorial $L^1$ Contraction, and Mixed-Norm Stability for Parabolic Systems with Rough Skew-Symmetric Potentials

We consider Dirichlet parabolic systems with measurable, real skew-symmetric zero-order potentials on bounded Lipschitz domains in three dimensions. Although skew-symmetry formally removes the potential from the energy balance, singular coefficients may leave the product $CU$ merely integrable, so t