Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform C^{1,√((4)/(3))-1-ε}∩ L² force

2025/05/27 by Córdoba, Diego, Laín-Sanclemente, Andrés, Martínez-Zoroa, Luis
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.20988

Abstract

We establish the existence of compactly supported solutions of the inviscid incompressible 2D Boussinesq equation with C^{1,√((4)/(3))-1-ε}∩ L² force that develop a singularity in finite time. Importantly, the force preserves this regularity at the blow-up time. Moreover, the forces in the vorticity and density equations have compact support. The mechanism behind the blow-up is an accumulated hysteresis effect on the vorticity caused by an infinite chain of "degenerate" pendula and flickering density.

Citations

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Related

• From Instability to Singularity Formation in Incompressible Fluids
• Finite-time Singularity Formation for Strong Solutions to the Boussinesq System
• Blowup in Stagnation-point Form Solutions of the Inviscid 2d Boussinesq Equations
• Blowup with vorticity control for a 2D model of the Boussinesq equations
• Numerical blowup in two-dimensional Boussinesq equations