Abstract
In this paper, we consider the asymptotic stability of the steady state with the constant equilibrium state. Under the assumptions that the \({H^3}\) norm of the initial data is small, but its higher-order derivatives could be large, we prove the global existence to the Cauchy problem for the asymmetric fluids in \({\mathbb{R}^3}\). Moreover, we obtain the time decay rates of the solutions and their higher-order spatial derivatives by introducing the negative Sobolev and Besov spaces.
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