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Global well-posedness for the 2D Boussinesq equations with a velocity damping term

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  • In this paper, we prove global well-posedness of smooth solutions to the two-dimensional incompressible Boussinesq equations with only a velocity damping term when the initial data is close to an nontrivial equilibrium state $ (0, x_2) $. As a by-product, under this equilibrium state, our result gives a positive answer to the question proposed by [1] (see P.3597).

    Mathematics Subject Classification: Primary: 35Q35; Secondary: 76B03.

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  • [1] D. AdhikarC. CaoJ. Wu and X. Xu, Small global solutions to the damped two-dimensional Boussinesq equations, J. Differential Equations, 256 (2014), 3594-3613.  doi: 10.1016/j.jde.2014.02.012.
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