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Quenching of flames by fluid advection
Peter Constantin, Alexander Kiselev, Leonid Ryzhik
We consider a simple scalar reaction-advection-diffusion equation with ignition-type nonlinearity and discuss the following question: What kinds of velocity profiles are capable of…
Bounds for Turbulent Transport
Peter Constantin
We present rigorous bounds for the average heat transport in Boussinesq Rayleigh-Benard convection.
The Euler Equations and Non-Local Conservative Riccati Equations
Peter Constantin
We present an infinite dimensional family of of exact solutions of the incompressible three-dimensional Euler equations. These solutions, proposed by Gibbon and Ohkitani, have infi…
Navier-Stokes equations and fluid turbulence
Peter Constantin
An Eulerian-Lagrangian approach to incompressible fluids that is convenient for both analysis and physics is presented. Bounds on burning rates in combustion and heat transfer in c…