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| Format: | Preprint |
| Veröffentlicht: |
2020
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| Online-Zugang: | https://arxiv.org/abs/2001.01662 |
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| _version_ | 1866929732536238080 |
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| author | Chanillo, Sagun Malchiodi, Andrea |
| author_facet | Chanillo, Sagun Malchiodi, Andrea |
| contents | We prove a conjecture in fluid dynamics concerning optimal bounds for heat transportation in the infinite Prandtl number limit. Due to a maximum principle property for the temperature exploited by Constantin-Doering and Otto-Seis, this amounts to proving a-priori bounds for horizontally-periodic solutions of a fourth-order equation in a strip of large width. Such bounds are obtained here using Fourier analysis, integral representations, and a bilinear estimate due to Coifman and Meyer which uses the Carleson measure characterization of BMO functions by Fefferman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_01662 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sharp bounds on the Nusselt number in Rayleigh-Bénard convection and a bilinear estimate via Carleson measures Chanillo, Sagun Malchiodi, Andrea Analysis of PDEs We prove a conjecture in fluid dynamics concerning optimal bounds for heat transportation in the infinite Prandtl number limit. Due to a maximum principle property for the temperature exploited by Constantin-Doering and Otto-Seis, this amounts to proving a-priori bounds for horizontally-periodic solutions of a fourth-order equation in a strip of large width. Such bounds are obtained here using Fourier analysis, integral representations, and a bilinear estimate due to Coifman and Meyer which uses the Carleson measure characterization of BMO functions by Fefferman. |
| title | Sharp bounds on the Nusselt number in Rayleigh-Bénard convection and a bilinear estimate via Carleson measures |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2001.01662 |