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Fronts in reactive convection: bounds, stability and instability
Peter Constantin, Alexander Kiselev, Lenya Ryzhik
We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. We establish nonlinear stability of planar fronts for narrow domains when the Rayleigh…
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…