SHARP BOUNDS ON ENSTROPHY GROWTH FOR THE VISCOUS BURGERS EQUATION

par Dr Nicola de Nitti (École Polytechnique Fédérale de Lausanne)

jeudi 25 janv. 2024, 13:30 → 14:30 Europe/Paris

E2290 (Tours)

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.