Invariant or quasi-invariant probability measures for infinite dimensional groups - Part I: Non-ergodicity of Euler hydrodynamic

被引：2
作者：
Malliavin, Paul
机构：
[1] Paris 75004
来源：
JAPANESE JOURNAL OF MATHEMATICS | 2008年 / 3卷 / 01期
关键词：
group of diffeomorphisms; Malliavin calculus; random unitary operator; existence of Euler flow;
D O I：
10.1007/s11537-008-0751-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Deterministic Euler flow on a torus cannot leave invariant any probability measure.
引用
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页码：1 / 17
页数：17
相关论文
共 11 条
[1]   Quasi-invariance of Brownian measures on the group of circle homeomorphisms and infinite-dimensional Riemannian geometry [J].
Airault, Helene ;
Malliavin, Paul .
JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 241 (01) :99-142
[2]   GLOBAL FLOWS WITH INVARIANT (GIBBS) MEASURES FOR EULER AND NAVIER-STOKES 2-DIMENSIONAL FLUIDS [J].
ALBEVERIO, S ;
CRUZEIRO, AB .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 129 (03) :431-444
[3]  
[Anonymous], 1990, CAMBRIDGE STUD ADV M
[4]   SUR LA GEOMETRIE DIFFERENTIELLE DES GROUPES DE LIE DE DIMENSION INFINIE ET SES APPLICATIONS A LHYDRODYNAMIQUE DES FLUIDES PARFAITS [J].
ARNOLD, V .
ANNALES DE L INSTITUT FOURIER, 1966, 16 (01) :319-&
[5]  
ARNOLD VI, 1998, APPL MATH, V125
[6]   Non-existence of infinitesimally invariant measures on loop groups [J].
Cruzeiro, Ana Bela ;
Malliavin, Paul .
JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (07) :1974-1987
[7]   Nonergodicity of Euler fluid dynamics on tori versus positivity of the Arnold-Ricci tensor [J].
Cruzeiro, Ana-Bela ;
Malliavin, Paul .
JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (07) :1903-1925
[8]   Brownian motion on volume preserving diffeomorphisms group and existence of global solutions of 2D stochastic Euler equation [J].
Cruzeiro, Ana-Bela ;
Flandoli, Franco ;
Malliavin, Paul .
JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 242 (01) :304-326
[9]  
Fukushima, 1980, DIRICHLET FORMS MARK, V23
[10]  
MALLIAVIN P, 2008, J FUNCT ANAL
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