Лекции проф. Клода Бардо, Университет Пьера и Марии Кюри (Париж, Франция)
C 31 мая по 3 июня 2010 г. в ИДСТУ СО РАН (к. 407) будет прочитан цикл лекций профессором Университета Пьера и Марии Кюри (Париж, Франция) Клодом Бардо.
EQUATIONS OF FLUID DYNAMIC FROM BOLTZMANN EQUATION TO TURBULENCE MODELLING
Prof. Claude Bardos
Professor Laboratory Jacques Louis Lions University Pierre et Marie Curie Paris, France
ABSTRACT: These 3 lectures are devoted to the mathematical treatment of fluid mechanic. This is an excellent subject for mathematicians because the underlining physic is very classical basic properties of molecules are well established. On the other hand due to the non linearity the mathematical analysis contain challenging problems which remain unsolved in spite of the contributions of Euler, Leray, Ladyzhenskaya and others: I will try to produce an overview mentioning technical issues but avoiding to deal in full details with these issues.
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31 мая 2010 г. 10.00 к. 407 |
ЛЕКЦИЯ 1: ИЕРАРХИЯ УРАВНЕНИЙ И НЕУСТОЙЧИВОСТЬ УРАВНЕНИЯ ЭЙЛЕРА HIERARCHY OF EQUATIONS AND INSTABILITY OF THE EULER EQUATION ABSTRACT: I will shortly describe a hierarchy of equation which stars from the Newtonian mechanic and ends with the models of turbulence. The goal is to show that the Euler equation is in the center of this hierarchy. Then I will show on simple and example the instabilities of the solutions of the 3d Euler equation. |
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1 июня 2010 г. 10.00 к. 407 |
ЛЕКЦИЯ 2: "ДИКИЕ" РЕШЕНИЯ DE LELLIS И L. SZKELYHIDI THE WILD SOLUTIONS OF DE LELLIS AND L.SZKELYHIDI ABSTRACT: The existence of very singular weak solutions of the Euler equation has already been observed by Scheffer and Shnirelman which in particular are of space-time compact support. However recently De Lellis and Szkelyhidi gave a construction of a residual set of such solutions inspired by the Nash Kuiper theorem in Riemannina geometry and using the differential inclusions of Tartar. |
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3 июня 2010 г. 10.00 к. 407 |
ЛЕКЦИЯ 3: ВЫВОД УРАВНЕНИЯ ЭЙЛЕРА ИЗ УРАВНЕНИЯ БОЛЬЦМАНА В НЕСЖИМАЕМОМ ПРЕДЕЛЕ, СЛЕДУЯ LAURE SAINT RAYMOND THE DERIVATION OF THE EULER EQUATION FROM BOLTZMANN EQUATION IN THE INCOMPRESSIBLE LIMIT FOLLOWING LAURE SAINT RAYMOND ABSTRACT: This very elegant derivation is coherent with the fact that coarser limits can be obtained whenever the properties of the limit model are well established. More precisely the result of Laure Saint Raymond is valid as long as the solution of the corresponding Euler equation remains smooth. |
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