Equilibrium statistical mechanics of barotropic quasi-geostrophic equations

被引:4
作者
Grotto, Francesco [1 ]
Pappalettera, Umberto [1 ]
机构
[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy
关键词
Quasi-geostrophic equations; channel flow; equilibrium statistical mechanics; weak vorticity formulation; white noise analysis;
D O I
10.1142/S0219025721500077
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to the first integrals energy and enstrophy are Gaussian measures supported by distributional spaces. We define a suitable weak formulation for barotropic equations, and prove existence of a solution preserving Gibbsian measures, thus providing a rigorous infinite-dimensional framework for the equilibrium statistical mechanics of the model.
引用
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页数:23
相关论文
共 19 条
[1]   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
[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]  
Albeverio S., 2008, Lecture Notes in Mathematics, V1942
[4]  
Azzam J, 2015, T AM MATH SOC, V367, P3095
[5]   THE BAROTROPIC QUASI-GEOSTROPHIC EQUATION UNDER A FREE SURFACE [J].
Chen, Qingshan .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (03) :1836-1867
[6]   ON THE WELL-POSEDNESS OF THE INVISCID MULTI-LAYER QUASI-GEOSTROPHIC EQUATIONS [J].
Chen, Qingshan .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (06) :3215-3237
[7]   Hopf bifurcation in quasi-geostrophic channel flow [J].
Chen, ZM ;
Ghil, M ;
Simonnet, E ;
Wang, SH .
SIAM JOURNAL ON APPLIED MATHEMATICS, 2003, 64 (01) :343-368
[8]   ORDINARY DIFFERENTIAL-EQUATIONS - NON-EXPLOSION AND QUASI-INVARIANT MEASURES [J].
CRUZEIRO, AB .
JOURNAL OF FUNCTIONAL ANALYSIS, 1983, 54 (02) :193-205
[9]  
DaPrato G., 2014, ENCY MATH ITS APPL, V152
[10]   DYNAMIC TRANSITIONS OF QUASI-GEOSTROPHIC CHANNEL FLOW [J].
Dijkstra, Henk ;
Sengul, Taylan ;
Shen, Jie ;
Wang, Shouhong .
SIAM JOURNAL ON APPLIED MATHEMATICS, 2015, 75 (05) :2361-2378