Blowup with vorticity control for a 2D model of the Boussinesq equations
arXiv:1608.01285
Abstract
We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a simplified vorticity stretching term and Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.
arXiv comment26 pages, 4 figures. Fixed some typos, expanded explanations
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