RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Search
RSS
Forthcoming seminars





You may need the following programs to see the files








Steklov Mathematical Institute Seminar
May 21, 2015 16:00, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)
 


On the Kelvin's 1880 problem and exact solutions of the Navier-Stokes equations

O. I. Bogoyavlenskij
Video records:
Flash Video 400.3 Mb
Flash Video 2,385.8 Mb
MP4 400.3 Mb

Number of views:
This page:1067
Video files:481
Youtube Video:

O. I. Bogoyavlenskij
Photo Gallery


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: Exact solutions to the steady equations of hydrodynamics are derived for that a classification of knots formed by the closed vorticity lines is obtained (Kelvin's 1880 problem).
Using the Alexander polynomial (that is a topological invariant of any knot in $\mathbb{R}^3$) it is shown which vortex torus knots are realized for the constructed exact solutions and which ones are not realized by the closed vorticity lines.
Exact solutions to the Navier-Stokes equations are obtained describing dynamics of a viscous incompressible fluid in $\mathbb{R}^3$. The presented solutions depend on an arbitrary vector field tangent to the 2-dimensional sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ and on an arbitrary measure on the sphere $\mathbb{S}^2$. It is shown that dynamics of fluid for these solutions is not turbulent either in the Eulerian or in Lagrangian senses in spite of the corresponding Reynolds numbers can be arbitrarily large.

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017