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Alexei Novikov : Diffusion in fluid flows

Enhacement of diffusion and reaction processes by advection is a classical subject that has been extensively studied by both physicists and mathematicians. In this talk I will consider reaction-diffusion on a bounded domain in the presence of a fast incompressible flow. I will also consider convective systems in a bounded domain, in which viscous fluids described by the Stokes system are coupled using the Boussinesq approximation to a reaction-advection-diffusion equation for the temperature. For such systems enhacement of diffusion implies, in particular, that the explosion threshold for power-like nonlinearities tends to infinity in the large Rayleigh number limit.

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