Global existence and decay estimate of solutions to magneto-micropolar fluid equations

We are concerned with magneto-micropolar fluid equations (1.3)-(1.4). The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the magneto-micropolarNavier-Stokes (MMNS) system, we obtain global existence and large time behavior of solutions near a constant states in R-3. Appealing to a refined pure energy method, we first obtain a global existence theorem by assuming that the H-3 norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms (H) over dot(-s) (0 <= s < 3/2) or homogeneous Besov norms (B)over dot(2),(-s)(infinity) (0 < s <= 3/2), we obtain the optimal decay rates of the solutions and its higher order derivatives. Do As an immediate byproduct, we also obtain the usual L-P - L-2 (1 <= p <= 2) type of the decay rates without requiring that the L-P norm of initial data is small. At last, we derive a weak solution to (1,3)-(1.4) in R-2 with large initial data. (C) 2018 Elsevier Inc. All rights reserved.