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Ergodicity for the Navier‐Stokes equation with degenerate random forcing: Finite‐dimensional approximation
Author(s) -
E Weinan,
Mattingly Jonathan C.
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.10007
Subject(s) - mathematics , forcing (mathematics) , degenerate energy levels , ergodicity , ergodic theory , navier–stokes equations , nonlinear system , galerkin method , mathematical analysis , statistical physics , physics , compressibility , mechanics , statistics , quantum mechanics
We study Galerkin truncations of the two‐dimensional Navier‐Stokes equation under degenerate, large‐scale, stochastic forcing. We identify the minimal set of modes that has to be forced in order for the system to be ergodic. Our results rely heavily on the structure of the nonlinearity. © 2001 John Wiley & Sons, Inc.