AVVISO:
>Il Prof. Claude Bardos terrà il seguente ciclo di lezioni presso il Centro
>De Giorgi (SNS), del quale sarà ospite:
>
>TITOLO: "Beliefs and Theorems for Fluid Mechanics"
>
> PROGRAMMA:
>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, October 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 emphasised.
>
> Tuesday, October 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 October20, 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 L^1 extension. The notion of
> dissipative solution for the incompressible Euler equation application to
> the incompressible limit of the Boltzmann equation.
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