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凸积分和合成湍流Convex integration and synthetic turbulence |
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| 课程网址: | http://videolectures.net/8ecm2021_szekelyhidi_convex_integration/ |
| 主讲教师: | László Székelyhidi Jr. |
| 开课单位: | 莱比锡大学 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | In the past decade convex integration has been established as a powerful and versatile technique for the construction of weak solutions of various nonlinear systems of partial differential equations arising in fluid dynamics, including the Euler and Navier-Stokes equations. The existence theorems obtained in this way come at a high price: solutions are highly irregular, non-differentiable, and very much non-unique as there is usually infinitely many of them. Therefore this technique has often been thought of as a way to obtain mathematical counterexamples in the spirit of Weierstrass’ non-differentiable function, rather than advancing physical theory; ”pathological”, ”wild”, ”paradoxical”, ”counterintuitive” are some of the adjectives usually associated with solutions obtained via convex integration. In this lecture I would like to draw on some recent examples to show that there are many more sides to the story, and that, with proper usage and interpretation, the convex integration toolbox can indeed provide useful insights for problems in hydrodynamics. |
| 关 键 词: | 凸积分; 可微函数; 流体动力学 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2022-03-24：hqh |
| 最后编审: | 2022-03-24：hqh |
| 阅读次数: | 124 |