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.
Vincent Perrollaz