[CvGmt News] seminario Bartolucci 22/10

[Daniele Castorina]

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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