[CvGmt News] Seminario D. Bartoluccii (22/11/2016)

[Alfonso Sorrentino]

SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"


Martedi' 22 novembre 2016, ore 14:30 Aula dal Passo

Daniele Bartolucci (Universita' di Roma "Tor Vergata")

Titolo: Global bifurcation analysis of mean field equations and the
Onsager microcanonical description of two-dimensional turbulence.

Abstract:
We discuss the solution of two long standing open problems closely related
to the mean field Liouville-type equation (P_\lm). On one side, we find
the global behaviour of the entropy for the mean field Microcanonical
Variational Principle ((MVP) for short), as it arise in the Onsager
description of two-dimensional turbulence on strictly starshaped domains
of second kind.
Among other things we find a region of strict convexity of the entropy. On
the other side, to achieve that goal, we have to catch the global
bifurcation diagram of solutions of the mean field equation (P_\lm),
emanating from \lm = 0 and crossing \lm = 8\pi.
The (MVP) suggests the right variable (which is the energy) to be used to
obtain a global parametrization of solutions of (P_\lm). In particular a
crucial  spectral simplification is obtained by using the fact that, by
definition, solutions of the (MVP) maximize the entropy at fixed energy
and total vorticity.


Website: http://www.mat.uniroma2.it/~sorrenti/SeminarioED.html


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