Journal
NONLINEARITY
Volume 34, Issue 1, Pages 509-531Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/abb1c6
Keywords
Rayleigh-Benard convection; global attractor; synchronization
Categories
Funding
- National Science Foundation [DMS-1418911]
- NSF [DMS-1818754]
- Einstein Visiting Fellow Program
- John Simon Guggenheim Memorial Foundation
- Simons Foundation [586788]
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The Rayleigh-Benard 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 proven to be equivalent to one with periodic boundary conditions and certain symmetries. A Gronwall estimate on enstrophy leads to bounds on the L-2 norm of the temperature gradient on the global attractor. By finding a bounding region for the attractor in the enstrophy-palinstrophy plane, all final bounds are algebraic in the viscosity and thermal diffusivity, which is a significant improvement over previously established estimates.
The Rayleigh-Benard 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 L-2 norm of the temperature gradient on the global attractor, which, in turn, is used to find a bounding region for the attractor in the enstrophy-palinstrophy plane. All final bounds are algebraic in the viscosity and thermal diffusivity, a significant improvement over previously established estimates. The sharpness of the bounds are tested with numerical simulations.
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