Differential and Integral Equations

Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics

Tonia Ricciardi Ricciardi and Gabriella Zecca

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Motivated by the mean field equations with probability measure derived by Sawada-Suzuki and by Neri in the context of the statistical mechanics description of two-dimensional turbulence, we study the semilinear elliptic equation with probability measure: \begin{equation*} -\Delta v=\lambda\int_IV(\alpha,x,v)e^{\alpha v}\,{\mathcal P(d\alpha)} -\frac{\lambda}{|\Omega|}\iint_{I\times\Omega}V(\alpha,x,v)e^{\alpha v}\,{\mathcal P(d\alpha)} dx, \end{equation*} defined on a compact Riemannian surface. This equation includes the above mentioned equations of physical interest as special cases. For such an equation we study the blow-up properties of solution sequences. The optimal Trudinger-Moser inequality is also considered.

Article information

Source
Differential Integral Equations, Volume 25, Number 3/4 (2012), 201-222.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012734

Mathematical Reviews number (MathSciNet)
MR2917882

Zentralblatt MATH identifier
1265.76005

Subjects
Primary: 76B03: Existence, uniqueness, and regularity theory [See also 35Q35] 35B44: Blow-up 76B44

Citation

Ricciardi, Tonia Ricciardi; Zecca, Gabriella. Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics. Differential Integral Equations 25 (2012), no. 3/4, 201--222. https://projecteuclid.org/euclid.die/1356012734


Export citation