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This paper is concerned with a time decay for unique global strong solution of a modified version of the tropical climate model originally derived by Frierson‐Majda‐Pauluis. We prove that false‖false(u,v,θfalse)‖L2false(R2false)→0 as t→∞ and obtain the decay rates with ts2false‖false(u,v,θfalse)false(tfalse)‖Hs→0 as t→∞, where s  ≥  0.

This paper is interested in the decay of solutions to 3D Navier–Stokes equations with a nonlinear damping term αfalse|ufalse|β−1u$$ \alpha {\left|u\right|}^{\beta -1}u $$. We discuss the bounds of the global strong solutions in the negative Sobolev space trueH˙−s$$ {\dot{H}}^{-s} $$ and establish the optimal decay rates in L2$$ {L}^2 $$ of the global strong solutions. Moreover, the upper bound of the derivative is also obtained. Finally, we investigate the asymptotic stability of the solutions to the system.

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