RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
Video Library
Archive
Most viewed videos

Search
RSS
New in collection





You may need the following programs to see the files






International scientific conference "Days of Classical Mechanics"
January 26, 2015 10:05–10:40, Moscow, Steklov Mathematical Institute of RAS, Gubkina, 8
 


KAM theory and the 3d Euler equation

S. B. Kuksin
Video records:
Flash Video 245.6 Mb
Flash Video 1,471.3 Mb
MP4 245.6 Mb

Number of views:
This page:471
Video files:247

S. B. Kuksin
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: Consider the Euler equation on a closed 3d manifold (e.g. on the 3-torus or on the 3-sphere). Let $u(t,x)$ be its solution, and $\omega(t,x)$ – the vorticity of this solution. By the Kelvin theorem the vorticity-vectorfields, calculated for different values of time, are conjugated by means of volume-preserving diffeomorphisms. Therefore the quantity $\kappa(\omega)$, equal to the volume of the set which is the union of all two-dimensional invariant tori of $\omega$ is time-independent. We use KAM and the Arnold theorem on the structure of steady-states of the 3d Euler to prove that $\kappa$ is continuous at $\omega$'s which are non-degenerate steady-states of the equation, and use this integral of motion to study qualitative properties of the dynamical system, defined by the equation in the space of sufficiently smooth vector-fields. Namely, to study its non-ergodicity and study the problem “does the manifold of steady-states of the equation attracts (in a suitable sense) all trajectories which start from its vicinity?”.
This is a joint work with B. Khesin and D. Peralta-Salas.

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020