Global existence and large time behavior of the asymmetric fluids

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.