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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Knots and links in fluid mechanics

## Knots and links in fluid mechanicsAdd to your list(s) Download to your calendar using vCal - Enciso, A (Instituto de Ciencias Matemticas; Madrid)
- Tuesday 24 July 2012, 09:45-10:05
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Topological Dynamics in the Physical and Biological Sciences In this talk I will discuss the existence of steady solutions to the incompressible Euler equations that have stream and vortex lines of any prescribed knot (or link) type. More precisely, I will show that, given any locally finite link L in R Time permitting, we will also very recent results on the topology of potential flows, that is, of steady fluids whose velocity field is the gradient of a harmonic function in R^3. These results are closely related to classic questions in potential theory that were first considered by M. Morse and W. Kaplan in the first half of the XX century and have been revisited several times after that, by Rubel, Shiota and others. The guiding principle of the talk will be that a strategy of “local, analysis-based constructions” + “global approximation methods”, fitted together using ideas from differential topology, can be used to shed some light on the qualitative behavior of steady fluid flows. Most of the original results presented in this talk will be based on the papers: A. Enciso, D. Peralta-Salas, Knots and links in steady solutions of the Euler equation, Ann. of Math. 175 (2012) 345-367. A. Enciso, D. Peralta-Salas, Submanifolds that are level sets of solutions to a second-order elliptic PDE , arXiv:1007.5181. A. Enciso, D. Peralta-Salas, Arnold’s structure theorem revisited, in preparation. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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