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 infinity 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.
Détails
Titre
Sharp bounds on enstrophy growth for viscous scalar conservation laws
Grant
N D N is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilit e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM); he was partially supported by the Alexander von Humboldt-Professorship program a Alexander von Humboldt-Professorship program Transregio 154 Project 'Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks' of the Deutsche Forschungsgemeinschaft: 2002023 NSF Postdoctoral Fellowship
