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| Approximating Stationary Statistical Properties |
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Citation： |
Xiaoming WANG.Approximating Stationary Statistical Properties[J].Chinese Annals of Mathematics B,2009,30(6):831~844 |
| Page view： 1822
Net amount： 1196 |
Authors： |
Xiaoming WANG; |
Foundation： |
the National Science Foundation (No. DMS0606671) and a 111 project from the
Chinese MOE. |
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| Abstract： |
It is well-known that physical laws for large chaotic dynamical systems are
revealed statistically. Many times these statistical properties of the system must be ap-
proximated numerically. The main contribution of this manuscript is to provide simple
and natural criterions on numerical methods (temporal and spatial discretization) that are
able to capture the stationary statistical properties of the underlying dissipative chaotic
dynamical systems asymptotically. The result on temporal approximation is a recent find-
ing of the author, and the result on spatial approximation is a new one. Applications to the
infinite Prandtl number model for convection and the barotropic quasi-geostrophic model
are also discussed. |
Keywords： |
Stationary statistical property, Invariant measure, Global attractor,
Dissipative system, Time discretization, Spatial discretisation, Uni-
formly dissipative scheme, Infinite Prandtl number model for convec-
tion, Barotropic quasi-geostrophic equations |
Classification： |
65P99, 37M25, 65M12, 37L40, 76F35, 76F20,
37L30, 37N10, 35Q35 |
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