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Abstract
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We study the global regularity of solutions to the 2D
Boussinesq equations with fractional dissipation, given by
in the velocity
equation and by
in the temperature equation. We establish the global regularity for
,
and
. This result is for the
subcritical regime
and the point here is to obtain the global regularity for the largest possible range of
.
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Keywords
Boussinesq equations, fractional dissipation, global
regularity
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Mathematical Subject Classification 2010
Primary: 35B65, 35Q35
Secondary: 76B03, 76A10
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Milestones
Received: 7 March 2017
Revised: 12 January 2018
Accepted: 25 May 2018
Published: 2 February 2019
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