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European Mathematical Society Publishing House
2024-03-29 06:10:18
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RLM&vol=23&iss=1&update_since=2024-03-29
Rendiconti Lincei - Matematica e Applicazioni
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.
RLM
1120-6330
1720-0768
General
10.4171/RLM
http://www.ems-ph.org/doi/10.4171/RLM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
23
2012
1
The 2-$D$ constrained $NS$ equation and stochastic vortex theory
Mario
Pulvirenti
Università di Roma La Sapienza, ROMA, ITALY
E.
Rossi
Università di Roma La Sapienza, ROMA, ITALY
Navier-Stokes equation, coherent structures, gradient flows, stochastic vortex theory
We consider a modified version of the two-dimensional NS equation introduced in [4], [5] preserving energy and momentum of inertia. The physical motivation of this approach is the occurrence of di¤erent dissipation time scales. The constraint we consider is related to the gradient flow structure of the 2-D Navier-Stokes equation with respect to the Wasserstein metric. In this paper we justify the choice of this metric from the point of view of the stochastic vortex theory.
Partial differential equations
Probability theory and stochastic processes
General
1
27
10.4171/RLM/614
http://www.ems-ph.org/doi/10.4171/RLM/614
A version of Gehring lemma in Orlicz spaces
Luigi
Greco
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Gabriella
Zecca
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Higher integrability, reverse Hölder’s inequalities, mappings of finite distortion
We present a version of the Gehring lemma, showing higher integrability in the scale of Orlicz spaces for a function $g$ satisfying reverse Hölder's inequalities of the type \[\left(\medint_B g^m\right)^{1/m}\le \medint_{2B}fg+\left(\medint_{2B} h^m\right)^{1/m},\] under suitable integrability conditions on $f$ which do not imply boundedness. We describe explicitly in the general case how the improved integrability of $g$ depends on the assumptions on $f$, thus extending results of [4, 2] which deal with $f$ exponentially integrable.\par We also present some applications of our result to the theory of mappings of finite inner distortion.
Real functions
Functions of a complex variable
General
29
50
10.4171/RLM/615
http://www.ems-ph.org/doi/10.4171/RLM/615
Poincaré series for maximal De Concini–Procesi models of root arrangements
Giovanni
Gaiffi
Università di Pisa, PISA, ITALY
Matteo
Serventi
Università di Pisa, PISA, ITALY
Models, arrangements, Poincaré series, roots
In this paper we focus on maximal complex De Concini–Procesi models associated to root arrangements of types A, B, C, D and we compute inductive formulas for their Poincaré series.
Algebraic geometry
Nonassociative rings and algebras
General
51
67
10.4171/RLM/616
http://www.ems-ph.org/doi/10.4171/RLM/616
Completeness of Reidemeister-type moves for surfaces embedded in three-dimensional space
Giovanni
Bellettini
Università di Roma 'Tor Vergata', ROMA, ITALY
Valentina
Beorchia
Università di Trieste, TRIESTE, ITALY
Maurizio
Paolini
Università Cattolica del Sacro Cuore, BRESCIA, ITALY
Isotopic embedded surfaces, apparent contours, completeness, Reidemeister moves
In this paper we are concerned with labelled apparent contours, namely with apparent contours of generic orthogonal projections of embedded surfaces in $\mathbb R^3$, endowed with a suitable information on the relative depth. We give a proof of the following theorem: there exists a finite set of elementary moves (i.e. local topological changes) on labelled apparent contours such that two generic embeddings in $\mathbb R^3$ of a closed surface are isotopic if and only if their apparent contours can be connected using only smooth planar isotopies and a finite sequence of moves. This result, that can be obtained as a by-product of general results on knotted surfaces and singularity theory, is obtained here with a direct and rather elementary proof.
Manifolds and cell complexes
General
69
87
10.4171/RLM/617
http://www.ems-ph.org/doi/10.4171/RLM/617
A spectral Schwarz lemma, II
Edoardo
Vesentini
Politecnico di Torino, TORINO, ITALY
Banach algebra, subharmonic function, spectrum, mumerical range
The spectral Schwarz lemma holding for any operator-valued holomorphic map of the open unit disc $\Delta \subset \mathbb{C}$ into the algebra of all continuous linear operators acting on a complex Banach space is extended to other scalar- and vector-valued gauges of continuous linear operators, with particular attention to the numerical range and the numerical radius of any continuous linear mapping acting on a complex Banach space.
Functions of a complex variable
General
89
95
10.4171/RLM/618
http://www.ems-ph.org/doi/10.4171/RLM/618