[CvGmt News] [Notiziario] [Settimanale] Centro De Giorgi: seminari del Prof. C. Bardos

Giulia Curciarello curciare at dm.unipi.it
Wed Oct 13 13:10:41 CEST 2004

Avviso di ciclo di lezioni del Prof. C. Bardos

TITOLO:  "Beliefs and Theorems for Fluid Mechanics"

To try to reach a convenient overview of the state of the art I intend 
in these three lectures to produce a mixture of both very formal 
constructions and rigourous theorems. Therefore I will follow the 
following schedule.

   Monday,  November 18, 16h30-18h30:  Aula Fermi Description of the 
hierarchy of equations from the Hamiltonian systems of Newton Mechanic 
to models of turbulence, with in between the Boltzmann and Navier Stokes 
equations. No proof of convergence is  given but the classical 
parameters of fluid mechanic are introduced and the role of entropy is 

 Tuesday, November 19,  16h30-18h30:  Aula Bianchi This lecture is 
devoted to the theorems concerning the incompressible Euler Equation. 
Local existence with smooth initial data in 3d,
  Global existence and uniqueness in 2d with initial bounded vorticity,
  Propagation of regularity in 2d  with the pair dispersion formula and 
in 3d  with the Beale Kato Majda Kozono criteria and the Constantin 
Fefferman criteria.
  Arnold stability criteria for stationary solutions.
  Open problems in particular weak limit of 2d solutions either with 
oscillating initial data or with vanishing viscosity and no slip 
boundary condition ( Kato criteria and Grenier instability.)

  Wednesday 20, 18h30-19h30: Aula Fermi  I describe tools used for the 
macroscopic limit of the Kinetic equations with the hope that they may 
be used also for other purpose. The averaging lemma of Golse Lions 
Perthame and Sentis and its L1 extension. The notion of dissipative 
solution for the incompressible Euler equation application to the 
incompressible limit of the Boltzmann equation.

Giulia Curciarello
Segreteria Didattica
tel: 050-2213219
e-mail curciare at dm.unipi.it
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