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Vortex layer cascades and finite time singularities for incompressible fluids

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If you have a question about this talk, please contact Zoe Wyatt .

We present a mechanism for finite time blow-up in the two-dimensional incompressible Boussinesq equations, achieved through a multi-layer degenerate pendula dynamics with a uniform $C^{1, \alpha}$ forcing term. The construction gives rise to a vortex layer cascade in which vorticity and temperature gradients concentrate successively, leading to singularity formation in finite time. We will outline the key ideas behind the cascade mechanism and discuss its implications for singularity formation in incompressible fluid equations. These results are joint works with Luis Martínez-Zoroa, Andrés Laín Sanclemente and Fan Zheng.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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Open Plan Area, BP Institute Average on weekdays: 9201.77997738 kWh Centre for Mathematical Sciences, Meeting Room 5 (centre building, basement).

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