Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Forthcoming seminars

You may need the following programs to see the files

Seminar on analytic theory of differential equations
October 26, 2016 14:30–16:00, Moscow, Steklov Mathematical Institute, Room 440 (8 Gubkina)

'On polynomial helicities in MHD"

P. M. Akhmet'ev
Video records:
MP4 2,607.7 Mb
MP4 661.4 Mb

Number of views:
This page:237
Video files:52

P. M. Akhmet'ev

Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: The helicity integral (in the form of the Hopf integral) plays an important role for equations of magnetic hydrodynamics (MHD). Its topological meaning was revealed by V.I. Arnold (1974) as the mean value of the asymptotic limit of Gauss integrals over pairs of magnetic lines.
In 2012 the author repeated Arnold's construction and defined the quadratic helicity integral. There was proposed a conjecture that solutions of standard MHD problems could be refined by using this integral. The conjecture was criticized by some authors and the main reasonings were the following: the quadratic helicity is not stable and it is reduced to the square of helicity under a $C^1$-small deformation of the magnetic field. The purpose of this talk is to respond to objections and confirm the conjecture. At the end, I will tell about the cubic magnetic helicities: they turned out to be eight, and five of them are not expressed via the helicity and quadratic helicity.

SHARE: FaceBook Twitter Livejournal
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018