Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1,\sqrt{\frac{4}{3}}-1-ε}\cap L^2$ force
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918133312258048 |
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| author | Córdoba, Diego Laín-Sanclemente, Andrés Martínez-Zoroa, Luis |
| author_facet | Córdoba, Diego Laín-Sanclemente, Andrés Martínez-Zoroa, Luis |
| contents | We establish the existence of compactly supported solutions of the inviscid incompressible 2D Boussinesq equation with $C^{1,\sqrt{\frac{4}{3}}-1-\varepsilon}\cap L^{2}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1,\sqrt{\frac{4}{3}}-1-ε}\cap L^2$ force Córdoba, Diego Laín-Sanclemente, Andrés Martínez-Zoroa, Luis Analysis of PDEs We establish the existence of compactly supported solutions of the inviscid incompressible 2D Boussinesq equation with $C^{1,\sqrt{\frac{4}{3}}-1-\varepsilon}\cap L^{2}$ 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. |
| title | Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1,\sqrt{\frac{4}{3}}-1-ε}\cap L^2$ force |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.20988 |