Sharp bounds on enstrophy growth for viscous scalar conservation laws

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 D. Ayala and B. Protas (Physica D, 2011), based on numerical evidence, for the viscous Burgers equation.

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