Invariant measures of Levy-Khinchine type for 2D fluids

被引：8

作者：

Albeverio, S ^{[1
]}

Ferrario, B ^{[1
]}

机构：

[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

来源：

PROBABILISTIC METHODS IN FLUIDS, PROCEEDINGS | 2003年

关键词：

D O I：

10.1142/9789812703989_0009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A survey of results on invariant measures of the Levy-Khinchine type for 2D Euler and stochastic Navier-Stokes equations is given. Uniqueness results of the corresponding Liouville respectively Kolmogorov flows are discussed. Stochastic dynamics associated with the invariant measures are also discussed (stochastic Stokes equation for the vorticity in the Gaussian case, Doob's independent Brownian motions process in the compound Poisson case).

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页码：130 / 143

页数：14

相关论文

共 22 条

[1] Analysis and geometry on configuration spaces: The Gibbsian case [J].

Albeverio, S ;

Kondratiev, YG ;

Rockner, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 157 (01) :242-291

[2] STATIONARY MEASURES FOR THE PERIODIC EULER FLOW IN 2 DIMENSIONS [J].

ALBEVERIO, S ;

RIBEIRODEFARIA, M ;

HOEGHKROHN, R .

JOURNAL OF STATISTICAL PHYSICS, 1979, 20 (06) :585-595

[3] CLASSICAL DIRICHLET FORMS ON TOPOLOGICAL VECTOR-SPACES - CLOSABILITY AND A CAMERON-MARTIN FORMULA [J].

ALBEVERIO, S ;

ROCKNER, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 88 (02) :395-436

[4] Uniqueness results for the generators of the two-dimensional Euler and Navier-Stokes flows - The case of Gaussian invariant measures [J].

Albeverio, S ;

Ferrario, B .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 193 (01) :77-93

[5] 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

[6] STOCHASTIC FLOWS WITH STATIONARY DISTRIBUTION FOR TWO-DIMENSIONAL INVISCID FLUIDS [J].

ALBEVERIO, S ;

HOEGHKROHN, R .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 31 (01) :1-31

[7]

ALBEVERIO S., 1993, STOCHASTIC PROCESSES, V7, P1

[8]

ALBEVERIO S, 2002, IN PRESS INFIN DIMEN

[9] CORRECTION [J].

BOLDRIGHINI, C .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1980, 78 (02) :303-303

[10] EQUILIBRIUM STATES FOR A PLANE INCOMPRESSIBLE PERFECT FLUID [J].

BOLDRIGHINI, C ;

FRIGIO, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1980, 72 (01) :55-76