图 书 馆
通过接触镜看欧拉流：普遍性和图灵完备性Looking at Euler flows through a contact mirror: Universality and Turing completeness |
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| 课程网址: | http://videolectures.net/8ecm2021_miranda_loking_euler/ |
| 主讲教师: | Eva Miranda |
| 开课单位: | 巴黎狄德罗大学 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [6, 7, 8] launched a programme to address the global existence problem for the Euler and Navier-Stokes equations based on the concept of universality. Inspired by this proposal, we show that the stationary Euler equations exhibit several universality features, in the sense that, any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the Euler equations on some Riemannian manifold of possibly higher dimension [1]. A key point in the proof is looking at the h-principle in contact geometry through a contact mirror, unveiled by Etnyre and Ghrist in [4] more than two decades ago. We end up this talk addressing a question raised by Moore in [5] : “Is hydrodynamics capable of performing computations?”. The universality result above yields the Turing completeness of the steady Euler flows on a 17- dimensional sphere. Can this result be improved? In [2] we construct a Turing complete Euler flow in dimension 3. Time permitting, we discuss this and other generalizations contained in [3]. This talk is based on several joint works with Cardona, Peralta-Salas and Presas. |
| 关 键 词: | 黎曼流形; 欧拉方程; 图灵完备性 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2022-03-24：hqh |
| 最后编审: | 2022-03-25：liyy |
| 阅读次数: | 28 |