Abstract
Abstract
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
∞
and total variation bounds and viscosity. This answers a conjecture by Ayala and Protas (2011 Physica D 240 1553–63), based on numerical evidence, for the viscous Burgers equation.
Funder
National Science Foundation
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics