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Blowup with vorticity control for a 2D model of the Boussinesq equations. (English) Zbl 1387.35066
Summary: 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 vorticity stretching term and a non-local 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.

MSC:
35B44 Blow-up in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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