Sharp bounds on enstrophy growth for viscous scalar conservation laws
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 (\e...
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| Sprache: | eng |
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| Zusammenfassung: | 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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| DOI: | 10.48550/arxiv.2308.06586 |