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[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"
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, 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
emphasised.
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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