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arXiv · 2308.06586

Sharp bounds on enstrophy growth for viscous scalar conservation laws

Dallas Albritton·Nicola De Nitti
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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 $L^\infty$ and total variation bounds and viscosity. This answers a conjecture by D. Ayala and B. Protas (\emph{Physica D}, 2011), based on numerical evidence, for the viscous Burgers equation.

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Dallas Albritton, Nicola De Nitti. 2023-08-12. Sharp bounds on enstrophy growth for viscous scalar conservation laws. https://arxiv.org/abs/2308.06586

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