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Cari colleghi,<br>
<br>
vi segnalo il prossimo seminario di Equazioni Differenziali a Tor
Vergata:
<h2><small>Martedi' 22 Ottobre 2013, h 14:15, Aula D’Antoni </small></h2>
<small>
</small>
<h2><small>Daniele Bartolucci (Università di Roma Tor Vergata)
</small></h2>
<small>
</small>
<h2><small>"Supercritical Mean Field Equations and the Onsager's
description of 2d-turbulence"<br>
<br>
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.</small></h2>
<br>
<br>
<br>
<br>
<pre class="moz-signature" cols="72">--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: <a class="moz-txt-link-abbreviated" href="mailto:castorin@mat.uniroma2.it">castorin@mat.uniroma2.it</a>
tel: +390672594653</pre>
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