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

DOI10.1007/s11537-008-0751-6zbMath1185.37157OpenAlexW2104162822MaRDI QIDQ1043871

Paul Malliavin

Publication date: 9 December 2009

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11537-008-0751-6

zbMATH Keywords

Malliavin calculusgroup of diffeomorphismsnon-ergodicityEuler flow

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Stochastic calculus of variations and the Malliavin calculus (60H07) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Cites Work

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• Brownian motion on volume preserving diffeomorphisms group and existence of global solutions of 2D stochastic Euler equation
• Quasi-invariance of Brownian measures on the group of circle homeomorphisms and infinite-dimensional Riemannian geometry
• Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids
• Topological methods in hydrodynamics
• Transfer of stochastic energy towards high modes and its application to diffeomorphism flows on tori
• Nonergodicity of Euler fluid dynamics on tori versus positivity of the Arnold-Ricci tensor
• Non-existence of infinitesimally invariant measures on loop groups

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