87,141 research outputs found
n the Ambjorn-Olesen electroweak condensates
No full textWe obtain sufficient conditions for the existence of the Ambjorn-Olesen [“On elec-
troweak magnetism,” Nucl. Phys. B315, 606–614 (1989)] electroweak N-vortices
in case N ≥ 1 and therefore generalize earlier results [D. Bartolucci and G. Taran-
tello, “Liouville type equations with singular data and their applications to periodic
multivortices for the electroweak theory,” Commun. Math. Phys. 229, 3–47 (2002);
J. Spruck and Y. Yang, “On multivortices in the electroweak theory I: Existence of
periodic solutions,” ibid. 144, 1–16 (1992)] which handled the cases N ∈ {1, 2, 3,
4}. The variational argument provided here has its own independent interest as it
generalizes the one adopted by Ding et al. [“Existence results for mean field equa-
tions,” Ann. Inst. Henri Poincare, Anal. Non Lineaire 16, 653–666 (1999)] to obtain
solutions for Liouville-type equations on closed 2-manifolds. In fact, we obtain at
once a second proof of the existence of supercritical conformal metrics on surfaces
with conical singularities and prescribed Gaussian curvature recently established by
Bartolucci, De Marchis and Malchiodi [Int. Math. Res. Not. 24, 5625–5643 (2011)].
C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4731239
Tempo angolano em Roma
No full textL'articolo si sofferma sulla produzione poetica legata alla città di Roma del poeta angolano Costa Andrade, in esilio in italia tra il 1961 e il 1962
Existence of stationary turbulent flows with variable positive vortex intensity
No full textWe prove the existence of stationary turbulent flows with arbitrary positive vortex
circulation on non-simply connected domains. Our construction yields solutions for
all real values of the inverse temperature with the exception of a quantized set, for
which blow-up phenomena may occur. Our results complete the analysis initiated
in Ricciardi and Zecca (2016)
Supercritical Mean Field Equations on convex domains and the Onsager's statistical description of two-dimensional turbulence
No full textWe 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 is a brand new achievement since 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 we 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, combining it with all the results obtained so far, we solve the Microcanonical Variational Principle in a small
range of supercritical energies where the entropy is shown to be concave
Le froid industriel / par L. Marchis,...
No full textCollection : Nouvelle collection scientifiqueContient une table des matièresAvec mode text
Prescribed Gauss curvature problem on singular surfaces
No full textWe study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface Σ admitting conical singularities of orders αi’s at points pi’s. In particular, we are concerned with the case where the prescribed Gaussian curvature is sign-changing. Such a geometrical problem reduces to solving a singular Liouville equation. By employing a min–max scheme jointly with a finite dimensional reduction method, we deduce new perturbative results providing existence when the quantity χ(Σ) + ∑_ i α_i approaches a positive even integer, where χ(Σ) is the Euler characteristic of the surface Σ
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