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, Ottobre 18, 16h30-18h30: 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, Ottobre 19, 16h30-18h30: 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, Ottobre 20, 18h30-19h30: 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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