[CvGmt News] seminario Bartolucci 22/10
Daniele Castorina
castorin at mat.uniroma2.it
Thu Oct 17 08:06:43 CEST 2013
Cari colleghi,
vi segnalo il prossimo seminario di Equazioni Differenziali a Tor Vergata:
Martedi' 22 Ottobre 2013, h 14:15, Aula D'Antoni
Daniele Bartolucci (Università di Roma Tor Vergata)
"Supercritical Mean Field Equations and the Onsager's description of
2d-turbulence"
We are motivated by the study of the Microcanonical Variational
Principle within the Onsager's description of two-dimensional
turbulence in the range of energies where the equivalence of
statistical ensembles fails. We obtain sufficient conditions for the
existence and multiplicity of solutions for the corresponding Mean
Field Equation on convex and thin enough domains in the
supercritical (with respect to the Moser-Trudinger inequality)
regime. This result is of independent interest, since general
existence results in the supercritical region were previously known
only on multiply connected domains. Then we study the structure of
these solutions by the analysis of their linearized problems and
also obtain a new uniqueness result for solutions of the Mean Field
Equation on thin domains whose energy is uniformly bounded from
above. Finally we evaluate the asymptotic expansion of those
solutions with respect to the thinning parameter and use it together
with all the results obtained so far to solve the Microcanonical
Variational Principle in a small range of supercritical energies
where the entropy is eventually shown to be concave. This is a joint
work with Francesca De Marchis.
--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: castorin at mat.uniroma2.it
tel: +390672594653
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