Algebraic bounds on the Rayleigh–Bénard attractor
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Peer-reviewed
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Abstract
The Rayleigh-B'enard system with stress-free boundary conditions is shown to
have a global attractor in each affine space where velocity has fixed spatial
average. The physical problem is shown to be equivalent to one with periodic
boundary conditions and certain symmetries. This enables a Gronwall estimate on
enstrophy. That estimate is then used to bound the
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Funder: John Simon Guggenheim Memorial Foundation; doi: https://doi.org/10.13039/100005851
Funder: Einstein Visiting Fellow Program
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1361-6544
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National Science Foundation (DMS-1418911 DMS-1818754)