Rigorous bounds on turbulent convection
Time: 03.12.2019, 11am -12pm
Room: 03.323 – Besprechungsraum Chair in Applied Analysis (Alexander von Humboldt-Professorship)
Rigorous bounds on turbulent convection
Prof. Camilla Nobili (Junior-Professor, Universität Hamburg Research Group DD)
We are interested in thermal convection as described by the Rayleigh-Bénard convection model.
In this model the Navier-Stokes equations for the (divergence-free) velocity u with no-slip boundary conditions are coupled to an advection-diffusion equation for the temperature T with inhomogeneous Dirichlet boundary conditions. The problem of understanding the (average) upward-heat-transport properties is of great interest for the applications and challenging for the rigorous analysis. We show how the PDE theory (in particular, regularity analysis) can contribute to the understanding of the scaling regimes for the heat transport. After reviewing the theory of Constantin& Doering ’99 we will present some recent results and discuss new challenges.