Journal
JOURNAL OF EVOLUTION EQUATIONS
Volume 21, Issue 3, Pages 2923-2954Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00028-020-00644-4
Keywords
Rayleigh-Benard convection; Rotational fluid flow; Cyclonic and anticyclonic coherent structures; Incompressible; Infinite Prandtl number; Global well-posedness; Weak solutions; Strong solutions
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Funding
- Einstein Stiftung Berlin, through the Einstein Visiting Fellow Program
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In this model, the dynamics of the velocity field occur at a much faster time scale than the temperature fluctuation, and the velocity field formally adjusts instantaneously to the thermal fluctuation at the limit. The global well-posedness of weak solutions and strong solutions to this model has been proven.
We analyze a three-dimensional rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number, i.e., when the momentum diffusivity is much more dominant than the thermal diffusivity. Consequently, the dynamics of the velocity field takes place at a much faster time scale than the temperature fluctuation, and at the limit the velocity field formally adjusts instantaneously to the thermal fluctuation. We prove the global well-posedness of weak solutions and strong solutions to this model.
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