We investigate asymptotic stability of certain stationary solution to the 3D Boussinesq equations with a velocity damping term in the domain Ω = R× (0,1). It is shown that as t→∞, the solution converges to the specific stationary solution with explicit algebraic rates in t as long as the initial data is close enough to it in some suitable Sobolev spaces of high order.
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Lihua Dong (2025) studied this question.
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