We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admissible by the L^infty and total variation bounds and viscosity. This answers a conjecture by D. Ayala and B. Protas (Physica D, 2011), based on numerical evidence, for the viscous Burgers equation. This talk is based on a joint work with D. Albritton.
