Séminaire d'analyse

SHARP BOUNDS ON ENSTROPHY GROWTH FOR THE VISCOUS BURGERS EQUATION
Nicola de Nitti (École Polytechnique Fédérale de Lausanne)
Thursday 25 January 2024 13:30 -  Tours -  E2290

Résumé :

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 (_Physica D_, 2011), based on numerical evidence, 
for the viscous Burgers equation. This talk is based on a joint work 
with D. Albritton. 
 

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